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1 Eectronic Commerce Research and Appications 8 (2009) Contents ists avaiabe at ScienceDirect Eectronic Commerce Research and Appications journa homepage: Forecasting market prices in a suppy chain game q Christopher Kiekintved a, *, Jason Mier b, Patrick R. Jordan a, Lee F. Caender a, Michae P. Weman a a Computer Science and Engineering, University of Michigan, 2260 Hayward Avenue, Ann Arbor, MI , USA b Department of Mathematics, Stanford University, Buiding 380, Stanford, CA 94305, USA artice info abstract Artice history: Received 17 October 2007 Received in revised form 4 November 2008 Accepted 5 November 2008 Avaiabe onine 28 November 2008 Keywords: Forecasting Markets Price prediction Trading agent competition Suppy chain management Machine earning Predicting the uncertain and dynamic future of market conditions on the suppy chain, as refected in prices, is an essentia component of effective operationa decision-making. We present and evauate methods used by our agent, Deep Maize, to forecast market prices in the trading agent competition suppy chain management game (TAC/SCM). We empoy a variety of machine earning and representationa techniques to expoit as many types of information as possibe, integrating we-known methods in nove ways. We evauate these techniques through controed experiments as we as performance in both the main TAC/SCM tournament and suppementary Prediction Chaenge. Our prediction methods demonstrate strong performance in controed experiments and achieved the best overa score in the Prediction Chaenge. Ó 2008 Esevier B.V. A rights reserved. 1. Introduction q This is a revised and substantiay extended version of a paper presented at the Sixth Internationa Joint Conference on Autonomous Agents and Mutiagent Systems (Kiekintved et a., 2007). * Corresponding author. Te.: E-mai addresses: ckiekint@umich.edu (C. Kiekintved), jmier@math.stanford. edu (J. Mier), prjordan@umich.edu (P.R. Jordan), aseep@umich.edu (L.F. Caender), weman@umich.edu (M.P. Weman). URLs: (C. Kiekintved), umich.edu/~prjordan (P.R. Jordan), (M.P. Weman). The quaity of economic decisions made now depend on market conditions that wi prevai in the future. This is particuary true of suppy chain environments, which evove dynamicay based on compex interactions among mutipe payers across severa tiers. We present and evauate methods of forecasting market conditions deveoped to predict prices in the Trading Agent Competition suppy chain management game (TAC/SCM). In TAC/SCM, automated trading agents compete to maximize their profits in a simuated suppy chain environment. They face many chaenges, incuding strategic interactions and uncertainty about market conditions. Though compex, this domain offers a reativey controed environment amenabe to extensive experimentation. TAC aso attracts a diverse poo of participants, which faciitates benchmarking and evauation. This is particuary important for prediction tasks, where the quaity of predictions depends in part on the actions of opponents. Research competitions such as TAC offer the opportunity to test predictions in environments where the opposing agents are designed and seected by others, mitigating an important source of potentia bias reative to using opponents of one s own design (Weman et a., 2007). Our agent for the SCM game, Deep Maize, reies on price predictions in both the upstream and downstream markets to make purchasing, production, and saes decisions. Fig. 1 shows an overview of the daiy decision process. Predictions about market conditions feed into an approximate optimization procedure that uses vaues to decompose the decision probem. The architecture is described in detai esewhere (Kiekintved et a., 2006). Since our predictions are integrated into a task-situated agent, we can evauate the benefits of improved predictions on overa performance in addition to prediction error metrics. We appy machine earning to forecast prices in two different markets with distinct negotiation mechanisms and information reveation rues. Like many rea markets, the avaiabe information on market conditions comes from a variety of heterogeneous sources. Integrating different earning techniques and representations to expoit a of the avaiabe information is a centra theme of our approach. We find that representing the current market conditions we is particuary important for effective earning. We begin with a discussion of reated work and an overview of the TAC/SCM game, highighting the benefits and drawbacks of the different forms of information avaiabe for making predictions. The first set of methods we describe are used for predicting prices in the downstream consumer market. Centra to a of these methods is a nearest-neighbors earning agorithm that uses historica /$34.00 Ó 2008 Esevier B.V. A rights reserved. doi: /j.eerap

2 64 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) Suppy Market Prediction Component Vaues Suppy Purchasing game data to induce the reationship between market indicators and prices. We test variations that empoy two different representations for price distributions: an absoute representation, and a reative representation that expoits oca price stabiity. Finay, we deveop an onine earning method that procedure that combines and shifts predictions using additiona observations within a game instance. Our evauation of these methods incudes both prediction error and suppy chain performance. We show substantia improvements over a baseine predictor, with onine adaptation exhibiting especiay strong performance improvements. We proceed to discuss methods for making predictions in the market for component suppies. There are two eements to our approach in this market. The first is a inear interpoation mode that uses recent observations to make reativey accurate predictions about the current spot market. The second is a earning mode that regresses prices against market indicators. This earning mode can be used to make absoute price predictions, or to predict residuas for the inear interpoation mode. We show that combining the inear interpoation mode for current market prices with residua predictions improves overa performance, particuary for ongterm predictions. We cose with discussion of the performance of both prediction agorithms based on the resuts of TAC/SCM tournaments and the inaugura TAC/SCM Prediction Chaenge. Deep Maize has been a perennia finaist in the primary competition, and paced first in the Prediction Chaenge. Our forecasting methods demonstrate strong performance on prediction error measures and contribute to strong overa performance in the context of decision-making. 2. Reated work State Estimation Long-term Production Schedue Factory Schedue Customer Market Prediction PC Vaues Customer Saes Market Predictions High-eve Decisions Low-eve Decisions Fig. 1. Overview of Deep Maize s decision process on each TAC/SCM day. Forecasting is studied across many discipines, and many approaches have been deveoped for making predictions based on historica data. We do not attempt to survey a of the various methods here, but refer the reader to one of many introductory texts that describe exponentia smoothing, GARCH, ARIMA, spectra anaysis, neura networks, Kaman fiters, and other popuar methods (Brockwe and Davis, 1996; Chatfied, 2001; Hastie et a., 2001). Pindyck and Rubinfed (1998) is a good introduction to many forecasting methods used in the context of economic predictions and modeing. The proiferation of techniques is in part an indication that the best method for any particuar probem may depend on many factors, incuding the type and quantity of information avaiabe and the properties of the domain. Many appications focus on comparing methods to identify the most effective approach for a particuar probem (for exampe, see the appication of forecasting to retai saes by Aon et a. or the appication to predict eectricity prices by Nogaes et a. (2002)). Our approach for price prediction focuses on combining predictions made using difference sources of information and methods. Various methods have been deveoped for combining predictions, often motivated by the probem of combining the opinions of experts (Bates and Granger, 1969; Cemen and Winker, 1999). Recenty, predictions markets have become a popuar method for aggregating information (Hanson, 2003). Our approach shares some features with these markets, incuding the use of ogarithmic scoring rues to evauate the quaity of predictions. Price forecasting is a very important eement of decision-making in a wide variety of market settings, incuding financia markets (Kaufman, 1998) and energy markets (Nogaes et a., 2002). The rise of internet auctions has ed to an increasing interest in computationa methods for price forecasting in auction environments (e.g., Ghani, 2005). Brooks et a. (2002) discusses many issues reated to earning price modes in the context of onine markets. Price prediction methods have aso been used as the basis for successfu bidding strategies in many specific types of auctions, incuding simutaneous ascending auctions (Osepayshvii et a., 2005). It is not surprising then that price prediction has payed an important roe in the design of agents for the Trading Agent Competition since its inception. For the TAC trave game (Weman et a., 2007), a crucia factor in agent performance was the abiity to predict the cosing price of auctions for hote rooms. Participants expored many approaches for making these predictions, spanning statistica anaysis, machine earning, and economic modeing (Cheng et a., 2005; Stone et a., 2003; Weman et a., 2004). Post-tournament anaysis reveaed that the common thread among the most effective methods was not the particuar technique appied, but rather the information taken into account by the predictor (Weman et a., 2004); specificay, the best predictors accounted for the initia auction prices. Most agents for the TAC/SCM game aso empoy some form of price prediction, but vary significanty both in what quantities are predicted and the methods used for making predictions. Many agents ony estimate prices for the current simuation day, and do not attempt to forecast changes in prices over time (Benisch et a., 2004, 2006; Burke et a., 2006; He et a., 2006). One of the most successfu agents in the tournament, TacTex, has appied a variety of sophisticated approaches for price prediction. The specific methods have evoved in successive tournaments, but generay rey on a combination of statistica machine earning appied to historica data and onine adaptation (Pardoe and Stone, 2005, 2006, 2007a,b). The most recent version of TacTex specificay uses machine earning to predict both current and future prices. The Minne- TAC team has aso devoted significant effort to deveoping prediction methods for the TAC/SCM domain (Ketter, 2007; Ketter et a., 2007). Their approach is somewhat unique in that it focus on predicting changes in the economic regimes, which refect oversuppy, under-suppy, or other characteristic market conditions. Our use of market state is simiar in spirit to the idea of an economic regime, but we do not distinguish among a discrete set of possibe regimes. The first version of Deep Maize used an anaytic soution based on competitive equiibrium to predict market prices (Kiekintved et a., 2004). This approach became infeasibe when the game rues were modified due to the greater compexity of the suppier pricing mode. Another unique approach was used by RedAgent, the winner of the first TAC/SCM competition (Keer et a., 2004). This agent used an interna market to coordinate decisions and make predictions; to our knowedge no current agents use this approach.

3 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) CPU Motherboard Memory HardDisk Pinte IMD Basus Macrostar Mec Queenmax Watergate Mintor component RFQ suppier offer offer acceptance 3. The TAC suppy chain game Agents in TAC/SCM pay the roe of persona computer (PC) manufacturers (Coins et a., 2007; Eriksson et a., 2006). 1 The six automated agents compete to maximize their profits on a simuated suppy chain, shown in Fig. 2. Agents assembe 16 different types of PCs for sae, defined by compatibe combinations of CPU, motherboard, hard disk, and memory components. Each day agents negotiate with suppiers to purchase components, negotiate with customers to se finished products, and create manufacturing and shipping schedues for the next day. Each agent has an identica factory with imited capacity for production. Each game has 220 simuated days, each of which takes 15 s of rea time The persona computer market The 16 PC types are separated into three market segments representing high-, mid-, and ow-grade PCs. The average demand eve for each segment varies separatey according to a random wak with a stochastic trend. Each day, the customer demand process generates a set of RFQs (request-for-quotes) representing the aggregate demand. Each customer request is vaid for a singe day and specifies a PC type, due date, reserve price, and penaty for ate deivery. The negotiations for these requests use a simutaneous seaed-bid auction mechanism. Agents submit price offers for a subset of the RFQs. The owest bidder for each request is awarded the order, and must deiver the product by the due date or pay the penaty specified in the contract. Due to the configuration of the market, there are strong interactions among auctions both within and across days The component market Agent 1 Agent 2 Agent 3 Agent 4 Agent 5 Agent 6 PCRFQ Customer To procure components to buid PCs, agents must negotiate with eight suppiers whose behavior is defined in the game specification. Each suppier ses two distinct grades of a singe component type. CPU components have a unique suppier, whereas a other types are provided by two suppiers. Suppiers have a imited daiy production capacity for each component they se. These capacities vary according to a mean-reverting random wak, and are not directy observabe by the manufacturers. Manufacturers negotiate with suppiers via an RFQ mechanism. Each day, a manufacturer may send up to five RFQs per component bid Fig. 2. TAC/SCM suppy chain configuration. 1 We present an overview of the game rues here. The fu rue specifications for each competition, tournament resuts, and genera TAC information are avaiabe at to each suppier specifying type, due date, quantity, and reserve price. Any future day may be specified as the due date. The suppiers respond the foowing day with offers specifying a proposed quantity, price, and deivery date. 2 Suppiers may opt to accept a subset of the offers by responding with orders. Suppiers determine offer prices based on the ratio of their committed and avaiabe production capacity. This pricing function accounts for inventory, previous commitments, future capacity, and the demand represented in the current set of customer RFQs. In genera, component prices rise as demand rises and suppiers become more constrained. In some cases, the suppier may be capacity constrained and unabe to offer components at any price. Prices depend on both the requested due date and the day the request is made. Price predictions must be made for this entire space of possibiities to support important decisions about the optima time to make component purchases Observabe market data Agents may utiize severa compementary forms of evidence to make predictions about market prices. Each provides unique insights into current activity and how the market may evove. The first category of evidence comprises observations of the markets during a game instance. This information is the most timey and specific to the current situation, but is of reativey ow fideity. More detaied observations of market activity are avaiabe in game ogs after each game instance has competed. 3 Logs from previous rounds are pubicy avaiabe, and additiona data may be generated in private simuations. During a game, agents receive daiy observations from participating in the PC and component markets. In the PC market, agents observe the set of requests and whether or not each bid resuted in an order. They aso receive a daiy report for each PC type isting the maximum and minimum seing price from the previous day. The detais of individua market transactions and opponents bids are not reveaed. In the component market, agents receive price quotes for each request they send, some of which may be price probes. Neither the suppier s state (inventory, capacity, and commitments) nor other agents requests are reveaed. Every 20 simuation days, manufacturers receive a report containing aggregate market data for the preceding 20-day period. This data incudes the mean seing price and quantity sod for each PC type, and the mean seing price, quantity ordered, and quantity shipped for component type. The report aso incudes the mean production capacity for each suppy ine. The importance of this evidence is that it is specific to the current market conditions and current set of manufacturing agents. However, these observations say reativey itte about how market conditions are ikey to evove, especiay if simiar conditions have not been observed earier in the game. The historica ogs revea the entire transaction history in each market (incuding a bids, offers, and orders), as we as suppier capacities and other state attributes hidden during a game instance. This precise information is potentiay very usefu for predicting the evoution of market prices over time. However, conditions in the current game are unikey to be identica to conditions in historica games. A particuary difficut issue is that the poo of competing agents is constanty changing as teams update their agents, so historica data may not be representative of the current strategic environment. Seecting reevant historica data is an important chaenge. 2 Suppiers may offer either a partia quantity or a ater deivery if they are unabe to meet the initia request due to capacity constraints. 3 A rue change in 2007 expicity disaows agents from coecting and utiizing these ogs during a tournament round, but ogs from previous rounds or simuations may sti be used.

4 66 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) Tabe 1 Four categories of predictions made in the Prediction Chaenge. Prediction Current PC prices Future PC prices Current component prices Future component prices Description 3.4. The Prediction Chaenge The 2007 TAC event introduced two chaenge competitions to compement the origina TAC/SCM scenario. In the TAC/SCM Prediction Chaenge (Pardoe, 2007), agents compete to make the most accurate price predictions in four categories: short- and ong-term, for both component and PC markets (see Tabe 1). The chaenge isoates the prediction component of the game by having participants make predictions on behaf of the same designated agent, PAgent. Simuations incuding a PAgent are run before the chaenge to generate og fies. During the chaenge, the og fies are used to simuate the experience of paying the game for the predictors by providing the exact sequence of messages observed by PAgent during the game. The predictions made based on this information by competitors in the chaenge do not affect the behavior of the PAgent. This simuation framework aows a predictors to make an identica set of predictions, and aso aows predictions to be made many times for the same set of game instances. The predictions are scored against actua prices using the root mean squared (RMS) error, normaizing by component and PC base prices. Each round of the chaenge used three sets of 16 game instances, with different agents competing with PAgent on the suppy chain. The agents comprising the competitive environment were seected from those in the pubic agent repository. 4 Since tests can be run independenty and repeated, the software framework for the chaenge aso provides a usefu tookit for conducting one s own prediction tests. We took advantage of this in deveoping and testing new prediction methods for the component market in preparation for the 2007 TAC/SCM tournament and Prediction Chaenge. 4. Methods for PC market predictions Lowest price offered by manufacturers for each current RFQ Median owest price offered for each PC type in 20 days Offer price for each component RFQ sent on current day Offer price for each component RFQ sent in 20 days Each day, Deep Maize estimates the underying demand state in the customer market and creates predictions of the price curves it faces. 5 For the current simuation day, the set of requests is known. Estimating the price curve in this case is equivaent to estimating the probabiity that a given bid on an RFQ wi resut in an order, denoted PrðwinjbidÞ. To predict the price curve for future simuation days, it is aso necessary to predict the set of request that wi be generated. We combine predictions about the set of requests and the distribution of seing prices for each request (i.e., PrðwinjbidÞ) to estimate the effective demand curve for each future day. The effective demand curve represents the expected margina seing prices for each additiona PC sod. The agent uses these forecast demand curves to make customer bidding decisions and create 4 The TAC agent repository stores binary impementations of many agents from past TAC tournaments, reeased by their deveopers. 5 The methods described in this section were deveoped for the 2005 TAC/SCM tournament, and used with minor updates and new data sets in the 2006 competition. The version used in the 2007 tournament and Prediction Chaenge were identica to the 2006 version (incuding the data sets). a projected manufacturing schedue. We begin by discussion of our methods for estimating a key eement of the game state, and proceed with a discussion of our methods for predicting customer market prices Customer demand projection The customer demand processes that determine the number of RFQs to generate exert a great infuence on market prices in the SCM game. There are three stochastic demand processes, corresponding to the respective market segments. Each process is captured by two state variabes: a mean Q and trend s. The number of RFQs generated in each market segment on day d is determined by a draw from a Poisson distribution with mean Q. The initia demand eves for each segment are drawn uniformy from known intervas. The mean demand evoves according to the daiy update rue Q dþ1 ¼ minðq max ; maxðq min ; s d Q d ÞÞ: Both the minimum and maximum vaues of Q are given for each market segment in the specification. The trend s is initiay neutra, s 0 ¼ 1, and is updated by the stochastic perturbation U½ 0:01; 0:01Š: s dþ1 ¼ maxð0:95; minð1=0:95; s d þ ÞÞ: ð2þ When the demand Q reaches a maximum or minimum vaue, the trend resets to the neutra eve. The state Q and s are hidden from the manufacturers, but can be estimated based on the observed demand. We estimate the underying demand process using a Bayesian mode, iustrated in Fig Note that the updated demand, Q dþ1, is a deterministic function of Q d and s d, as specified in Eq. (1). This deterministic reationship simpifies the update of our beiefs about the demand state given a new observation. Let PrðQ d ; s d Þ denote the probabiity distribution over demand states given our observations through day d. We can incorporate a new observation b Q dþ1 as foows: PrðQ d ; s d j b Q dþ1 Þ/Prð b Q dþ1 jq d ; s d ÞPrðQ d ; s d Þ: Eq. (3) expoits the fact that the observation at d þ 1 is conditionay independent of prior observations given the demand state ðq d ; s d Þ. We can eaborate the first term of the RHS using the demand update (1): Prð b Q dþ1 jq d ; s d Þ¼PoissonðminðQ max ; maxðq min ; s d Q d ÞÞÞ: After cacuating the RHS of Eq. (3) for a possibe demand states, we normaize to recover the updated probabiity distribution. We can then project forward our beiefs over ðq d ; s d Þ using the demand and trend update Eqs. (1) and (2), to obtain a probabiity distribution over ðq dþ1 ; s dþ1 Þ. A sequence of updates by Eq. (3) represents an exact posterior distribution over demand state given a series of observations. To maintain a finite encoding of this joint distribution, we consider ony integer vaues for demand and divide the trend range into T discrete vaues, eveny spaced (Deep Maize uses T ¼ 9 for tournament pay). Given a distribution over demand states, we can project this distribution forward to estimate future demand Learning prices from historica data We use a k-nearest-neighbors (k-nn) agorithm to induce the reationship between indicators of market conditions (features) and ikey distributions of current and future prices. The idea is 6 We have reeased source code for this estimation method. It is avaiabe in the TAC agent repository. ð1þ ð3þ

5 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) simpe: given a set of games, find situations that most cosey resembe the current situation and predict based on the observed outcomes. When prices are not changing much from day to day, earning prices from historica data has itte additiona benefit over simpy estimating the prices in the current game instance. However, when prices are changing, historica data may hep the agent to predict how the prices wi move based on features of the current situation. For each PC type and day, we define the state using a vector of features F ¼ðf 0 ;...; f n Þ. 7 The difference between two states f 1 and f 2 is defined by weighted Eucidean distance: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ux n d ¼ t w i ðf 1 i f 2 i Þ 2 ; i¼0 τ d Q d τ d+1 Q d+1 where w i is a weight associated with each feature. Additionay, we bound the maximum distance for any individua feature, so d ¼1if f 1 i f 2 i is greater than the bound. To predict the prices during a game, the agent first computes the current state features. It then finds the k state vectors in a database of historica game instances that are most simiar to the current state, using d as the metric. To ensure diversity in the data set, we seect at most one of the k vectors from each historica game instance. Associated with each state in the historica database are the observed price distributions in that game instance. We average these for the k observations to predict prices in the current game. Preiminary experiments varying the vaue of k showed the best resuts for vaues between 15 and 20; we use a vaue of 18 for a competitions and experimenta resuts presented beow. The potentia features we experimented with incuded the current simuation day, statistics about current prices, and estimates of underying suppy, demand, and inventory conditions. Many of these were motivated by anaysis showing that reated measures were strongy correated with customer market prices in previous competitions (Kiekintved et a., 2005). We tested a range of possibe features, weights, and bounds in preiminary experiments, and seected those which had the owest prediction error after extensive but ad hoc manua exporation. A of the foowing resuts use equa weights and bounds. For predicting the current days prices, we seected the foowing features: average high and average ow seing price from the previous five days, estimated mean customer demand (Q), the simuation day, and the inear trend of seing prices from the previous ten days. For predicting future prices, we used the same set of features with the addition of the estimated customer demand trend (s) Data sets We empoy two distinct data sets for making predictions, one based on tournament games and one based on interna simuations. The tournament data set contained games from earier rounds in the tournament. As new rounds were payed, we added #Q Fig. 3. Bayesian network mode of demand evoution. 7 When initiay computing the vaues of features, we normaize the vaues for each feature by the standard deviation of the feature in the training set. the additiona games to the training set. During the 2005 tournament we automaticay added new games within a round to the data set; this was disaowed by the 2007 rue change mentioned above. The second data set consisted of games run using six copies of Deep Maize. We payed a sequence of roughy 100 games, initiay using just the tournament data set to make predictions. After each game, we repaced the odest og in the data set with the new one, so eventuay the data set consisted entirey of games payed by the six Deep Maize agents. The fina 45 games of this sequence were seected as the sef-pay data set. Ideay, as the data sets contain more data from this specific environment, the predictions wi come to refect the true market prices and agents behavior wi improve. In the imit, we can imagine agents converging to a competitive equiibrium, which may be coser to the environment of the fina round than games from ess competitive rounds eary in the tournament. As it happened, our anaysis indicates that predictions based on this data set were not very accurate Representing and estimating price distributions We experiment with two different representations for the distribution of PC prices. One uses absoute price eves, and the other is reative to recent price observations. The advantage of absoute prices is that they transate readiy across games and can easiy represent changes in the overa eve of prices. The reative distribution is centered on moving averages of the high and ow seing price reports for the previous five days. Between these two averages we use 60 uniformy distributed points, above the average of the highs and beow the average of the ows we use 20 points distributed uniformy. The strength of this representation is in its abiity to expoit the fact that prices tend to be stabe over short periods of time in the game (a few simuation days). It effectivey shifts observations from historica games into the reevant range of prices for the current game, which is often sma. When extracting data from historica games we adjust for the number of opponent agents by randomy seecting one agent and removing that agent s bid, if it exists. This accounts for the effects of the agent s own bid on the price; it is effectivey earning the price that woud be expected based on ony the competitors bids. We aso smooth the observed distributions by considering a requests in the range d 10;...; d þ 10. To compute the estimated price distribution we take the average of the distributions stored for the k-nearest-neighbors, as described above. For each price point j, we take the predicted probabiities for this point in each of the historica instances and average them. For reative predictions, these points represent pricing statistics reative to current prices; for absoute, they represent absoute prices. After averaging, we enforce monotonicity in the distribution. Starting from the ow end of the distribution, we take the maximum of the estimated probabiity for the price point and the estimated probabiity of the immediatey preceding price point. To forecast prices i days into the future, we project based on what happened i days into the future in each historica game. The agent requires predictions for a future days, so using this method requires that the historica instances have at east as many days remaining in the game as the current game does. We enforce the tighter constraint that the historica predictions must start on exacty the same simuation day. For reative price predictions, we aso account for changes in the overa price eves over time by modifying the pricing statistics. For each price statistic, we compute the average change over the intervening i days in the historica data. Pricing statistics for the future days are modified by adding the average change. The absoute distributions do not need

6 68 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) to account for this, since the price points are based on absoute vaues Onine earning We empoy an onine earning procedure that optimizes predictions according to a ogarithmic scoring rue. 8 First, we produce baseine predictions P tournament and P sef-pay based on the two data sets described in Section We then construct adjusted predictions of the form aðb P tournament þð1 bþp sef-pay Þþc; ð4þ where b weights the two prediction sources based on their accuracy in the current environment, and the coefficients a and c define an affine transformation aowing us to correct for systematic errors. We determine the vaues of a, b and c using a brute-force search to find the set of vaues (from a discretized range) that minimizes the scoring rue. The possibe transformations are scored using the recent history of bids won and ost, a vauabe but otherwise unused source of information. Each possibe set of vaues is scored on the measure P ogða bids bidþ where a bid is the magnitude of the difference between the predicted probabiity of winning and the resut of the bid, which is 1 if the bid resuted in a win and 0 otherwise. To prevent very arge changes in the prediction we oosey bound the possibe vaues of a, b and c. This optimization is performed using the actua bids submitted by the agent in recent days, and modifies the distribution ony within the range of prices where bids are made. This typicay eaves the extremes of the distribution (very high or ow probabiity bids) unchanged, since there is itte bidding activity at these extremes. 5. Evauation of PC market predictions We evauate our forecasting techniques using both prediction error and suppy chain performance. We evauate severa variations of the predictor that empoy subsets of the functionaity described in Section 4 to assess the contributions of each. As a baseine we use a heuristic predictor described by Pardoe and Stone (2005). The baseine predictor uses ony information contained in the current price eve, and reies competey on oca price stabiity for predictive power. This is simiar to what our predictor might ook ike using the reative representation without any historica data or onine transformations. This predictor produces surprisingy accurate predictions despite its simpicity. The reason is that prices in the TAC SCM game tend to be quite stabe for ong periods, especiay if the start and end game conditions are excuded. 9 One of the primary reasons we use this as a baseine is that we beieve it is refective of the defaut heuristic methods used by many of the agents to make decisions (especiay in the eary years of the competition). In particuar, it makes use of ony oca information about prices in the current game, and does not attempt to project changes in price eves over time. The baseine method predicts the distribution of PC prices using a weighted average of uniform densities between the ow and high prices from the previous five days. 10 We project this into the future by assuming that the distribution of prices does not change and 8 The ogarithmic scoring rue is stricty proper, in that the optima score is obtained ony for the true probabiity. Scoring according to rues that are not proper (incuding RMS error) can ead to biased estimates. 9 A inear regression on the average seing prices from one day to the next resuts in an R 2 vaue on the order of 0.99, so current prices are extremey predictive of prices in the near future. 10 We use weights of 0.3 for the most recent two days, 0.2 for the midde day, and 0.1 for the odest two days. adjusting for the predicted change in the number of RFQs generated, as given by the mode of customer demand described in Section 4.1. We present resuts for the baseine and four variations of our k- NN-based predictor. These variations use either the reative or absoute representation, and either appy onine affine transformations or not. A resuts use both the tournament and sef-pay data sets, which contain 95 and 45 game instances respectivey. Regardess of whether overa affine transformations are appied we use the onine scoring method to weight the predictions from these two sources. At the end of this section we briefy discuss the effects of varying the data sets. A error resuts are derived from the 14 cean finas games from the 2005 tournament Prediction error We discuss two different types of prediction error. The first is for predictions made about the probabiity of winning the current day s auctions, and the second is for predictions about the effective demand curve on future days. As we discuss the prediction error resuts, it is important to keep in mind that there is a substantia amount of uncertainty inherent in the domain mode; we do not expect any prediction method to achieve anywhere near perfect predictions. To demonstrate this and provide some caibration, we consider the process that generates the overa eve of customer demand in the SCM game. The eve of customer demand (number of requests generated each day) is one of the most important factors infuencing market prices. Reca that we use a Bayesian mode to track the mean customer demand and trend; this mode is the theoreticay optima predictor of the process. We ran tests comparing this predictor to a naive predictor that predicts that the mean demand on a future days wi remain exacty the demand observed today. The optima Bayesian mode improved on the naive mode, but the difference was reativey sma. The naive mode had an RMS error of approximatey 35, and the Bayesian mode achieved an RMS error of approximatey 30 a reduction on the order of 15%. Whereas this may seem a reativey sma improvement in prediction quaity, these sma improvements can transate into substantia differences in overa agent performance Current day prediction error Predicting the conditiona distribution PrðwinjbidÞ for the current day s RFQ set is an important specia case because these estimates are used for making bidding decisions. It is aso unique because it is the ony day for which we have the actua set of customer RFQs avaiabe; for future days, there is substantia additiona uncertainty since the quantities, PC types, due dates, penaties, and reserve prices are a unknown. We measure RMS error over a range of possibe prices (i.e., potentia bid vaues). The error may vary over the distribution, and this aows us to present a more detaied picture of the errors each predictor makes. The range of vaues we consider is reative to the recent high and ow seing prices in the game. We distributed 125 price points over the range from 10% beow the average ow seing price from the previous five simuation days, to 10% above the average of the high seing price over the same window. Bids towards the high and ow ends of this distribution are very rare, since they are either very high or ow reative to the market. Deep Maize s bids are centered around price point 62, with a arge majority faing between price points 50 and In two games (3718 and 4254) the University of Michigan network ost connectivity and this team s agent was unabe to connect to the game server for a arge part of the game. This distorts the resuts for uninteresting reasons, so we omit these games.

7 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) RMS Error Reative with onine earning Reative Absoute with onine earning Absoute Baseine Heuristic Optima Distribution Current Day Prediction Error Reative Price Fig. 4. RMS prediction error for current day predictions in the TAC/SCM fina round games. The points on the horizonta axis represent a uniform distribution of points over a range defined by the recent high and ow seing prices in the market. To compute the error measure, we process each RFQ separatey. For each of the 125 price points, we measure the error as the difference between the predicted probabiity and the actua outcome. The outcome is either 1 if the owest bid was higher than the price point, or 0 if the owest bid was ower than the price point (corresponding to whether a bid at that price woud have won or ost the auction). A subtety of measuring error based on individua RFQs in this way is that any probabiistic prediction that is not either 1 or 0 wi, by definition, show error on this measure. To provide a benchmark for this effect, we aso pot the error for the optima distribution. This is a distribution derived from the actua prices for the PC type and day being measured, but without RFQ-specific features. Fig. 4 shows the resuts of this error measure computed for each of the five candidate predictors, as we as the optima distribution. We compute errors averaged over a games from the 2005 tournament fina round, restricted to predictions made for the midde part of the game from simuation day 20 to 200. This restriction is primariy because the baseine predictor is not designed for border cases, such as when no recent price observations are avaiabe. The error of the baseine is artificiay high in these cases, which woud distort the overa error resuts in favor of our methods. Of the candidate predictors, the reative predictor with onine earning has the owest overa prediction error. A four of our predictors have ower error than the baseine in the center part of the distribution. The two absoute predictors have greater error when making predictions for very high or very ow prices. Onine earning reduces prediction error across the entire distribution for both the absoute and reative representations. The reative predictors generay perform better than the absoute predictors. However, the absoute predictor with onine earning has ower error than the reative predictor without onine earning in the center of the price distribution. This is where onine earning shoud have the greatest impact, since more bids are paced in this region and it has more data to make updates. The differences in error between our predictors and the baseine are quite substantia. In the center of the distribution, the difference between the baseine method and the optima method is 0.3, and the difference between the optima and the reative predictor with onine earning is 0.2, an improvement of roughy 30%. Conceptuay, errors towards the center of the distribution are ikey to be much more important because bids are centered there. However, is not cear how errors shoud be weighted, since bid densities may vary in different situations (and certainy for different agents). These predictions are aso used for making non-bidding decisions, which may use the information in different ways. Using suppy chain performance (as we do in Section 5.2 beow) is one way to resove this diemma, since we can test the predictors as they are used by a rea decision-making procedure Future forecasting error A distinctive feature of Deep Maize is that it expicity forecasts changes in future market conditions. For future days, the agent transates its predictions into an effective demand curve for use in production scheduing. This demand curve specifies the price the agent woud need to bid to win a particuar quantity of PCs, on average. These prices are given in an ordered ist, with the first price representing the bid to win one PC, the second price the bid to win two PCs, and so on. The predictor gives the probabiity of winning a bid Prðwin;jbidÞ, which we combine with the predicted overa demand to determine the expected quantity won for any given bid eve. Inverting this function yieds the desired prices. 12 We measure the error for this effective demand curve, which combines errors from the price predictions and demand predictions. For each simuation day, we compute the actua demand curve by sorting the observed prices for each PC. We then measure the RMS error between the prices in this ist and the predicted demand curve, summing the errors for each PC in the ist up to a maximum of 200 vaues per day. 13 Fig. 5 compares the five predictors on this aggregate measure of future forecasting error out to a prediction horizon of 50 days. The pattern of resuts is simiar to the resuts for the current day. The two reative predictors score the best over a horizons, foowed by the baseine and then the two absoute predictors. The onine affine transformations are beneficia regardess of the representation used. We note that this measure averages error over the distribution (each data point represents a compression of the fu distribution shown in Fig. 4). We present information in this way partiay for easy visuaization, but aso because future 12 Our functiona form aows simpe inversion of this function, but this inversion can aso be computed using a simpe binary search to find the necessary bid eve. 13 An agent typicay projects seing 100 or fewer PCs of any type on a given day, so this is roughy twice the number of vaues the agent actuay uses to make decisions.

8 70 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) RMS Error Reative with onine earning Reative Absoute with onine earning Absoute Baseine Heuristic panning may be more dependent on errors over the entire distribution than bidding decisions. However, we shoud note that the absoute predictor shows higher overa error on this measure primariy because of errors at the extreme parts of the distribution, as in the short-term error resuts Suppy chain performance Future Prediction Error Since our forecasting methods were specificay designed to support decision-making in a fuy impemented and automated agent, we have the opportunity to assess how forecasts impact agent performance. This is particuary interesting because of the compex interactions between prediction error and decisions. As discussed above, it can be difficut to determine how to weight different types of prediction errors. Another issue with onine predictions is that the decisions made affect the information avaiabe for making future predictions. We ran simuations using a profie of two MinneTAC-05 agents, two TacTex-05 agents, one static version of Deep Maize, and one modified version. MinneTAC-05 and TacTex-05 were finaists in 2005 that were among the first to reease agent binaries. We ran four sets of games with a minimum of 35 sampes. The static version of Deep Maize used the reative affine predictor. We present resuts as differences between the static and variabe versions of Deep Maize. This pairing reduces variance but introduces bias to the extent that varying the sixth agent affects the performance of the static version. Another important caveat is that these resuts are for a singe profie of strategies. More systematic approaches to seecting test environments may be better justified on gametheoretic grounds (Jordan et a., 2007), but we make do with a singe convenient abeit ad hoc profie here. In addition to scores we give three measures of customer saes performance: average seing price (ASP), seing efficiency, and timing efficiency. Seing efficiency is the fraction of achieved revenue to the maximum possibe revenue for identica daiy saes, given perfect information about opponents bids and the option to partiay fi orders. Timing efficiency measures how we the agent distributed saes over time. Let the t-optima same day seing price be the highest ASP the agent coud achieve by seing each PC at most t days after it was actuay deivered and no earier than it was actuay produced. PCs are abeed according to a FIFO queuing poicy. Timing efficiency is the ratio of the t-optima same day seing price to the seing efficiency. This factors out the effects of bidding poicy and eaves the effects of deciding which days to se on. The appea of these additiona metrics is that they aow us to compare a specific eement of decision performance against an optima vaue, though we must remain cognizant of the additiona constraints when interpreting the resuts Prediction Horizon (days) Fig. 5. RMS error between predicted and actua effective demand curves out to a horizon of 50 days, computed on the 2005 finas. Tabe 2 Performance measures in simuated games. The numbers represent the difference between two versions of Deep Maize using the reative affine predictor and the indicated predictor. Predictor Score ASP Seing efficiency 20-Day timing Reative, no affine 2.3 M Absoute, affine 0.3 M Absoute, no affine 1.2 M Baseine 9.1 M The simuation resuts are in Tabe 2. The most striking point is that a of our k-nn-based predictors comfortaby outperform the same agent using the baseine predictor. To caibrate, the difference between the top and bottom scores in the 2005 finas was 6.5 M, ess than the advantage of any of our predictors over the baseine. Ceary, effective prediction can have a sizabe impact on agent performance when the decision-making architecture is capabe of expoiting the information. The affine transformations again showed benefits for both representations. The absoute predictors scored better than the reative predictors, abeit by fairy sma margins. This is somewhat unexpected, given the error resuts. Earier resuts using a smaer data set for the predictors actuay showed a sight advantage for the reative predictor. We expect a arger data set to benefit the absoute representation disproportionatey because some of the features are based on current prices. With more data more simiar instances are avaiabe, and the absoute representation shoud predict more ike the reative representation. We conjecture that the reative representation may have greater advantages for smaer data sets, but have not verified this experimentay. Another ikey expanation for this discrepancy is that the absoute representation better refects the actua uncertainty present because it is abe to spread predictions over a broader range of prices. This may cause the agent to deay making purchasing decisions unti more information is avaiabe, potentiay improving performance. In genera, the differences between the agent variations on the saes metrics are reativey sma, but we note some interesting features. The timing measure correates quite we with the overa scores. The baseine predictor performs very poory on this measure as we as having a ow ASP. The seing efficiency numbers do not show a strong pattern, and the ASP numbers for the k-nn variations are aso ambiguous. This suggest that one of the more consistent benefits of better forecasts for Deep Maize is the usefuness of these forecasts in timing saes activity Tournament and sef-pay data We aso generated error scores for the four predictor variants using ony the tournament data set and ony the sef-pay data set (a tota of 12 different variations). We do not present fu data here, but can describe the pattern of resuts fairy easiy. Using ony the tournament data resuted in amost exacty equivaent performance to using the combined data sets. The resuts using ony the sef-pay data were amost aways worse than either the tournament ony or combined settings. One concusion we draw from this is that the process we used to generate the sef-pay data did not produce the most reevant experience for making predictions. Another is that the onine scoring procedure was effective at detecting the source of more saient information to use in the combined predictor. It does this by pacing a very high vaue on the variabe b in Eq. (4), weighting the tournament data set much more heaviy than the sef-pay data set. As the agent pays a game, we often observe vaues set to the maximum possibe vaue, within the range of aowabe vaues.

9 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) Price Reative to Base Price Current Day Reative Due Date Fig. 6. Sampe price predictions p i;iþd ð1þ for a singe component where i is the current day and d is the reative due date. Price Day Due Fig. 7. A sampe inear interpoation of recent price quotes. 6. Methods for component market predictions As for the PC market, Deep Maize uses price forecasts to determine how to procure components in the suppy market. Component price forecasts take the form p ðs;cþ i;j ðqþ, denoting the predicted offer price for a quantity q of component type c, requested from suppier s on day i, with due date j. The price predictions for each possibe pair of request date and due date form a surface, as depicted in Fig. 6. These prediction are made each day for each suppier-component pair ðs; cþ. This contrasts with the PC market, where we mode a price curve with a singe time parameter (the request date). 14 Each day, manufacturers receive offers from suppiers in response to the RFQs sent the previous day. Information from these offers may be used as input to price predictions. Note that it is generay not possibe to get a direct price quote for each future date, due to the imitation of five RFQs per day for each suppier and component combination. Thus, there is significant uncertainty regarding even the current price curve. We consider three casses of prediction methods for the component market. The first creates an estimate of the current price curve using the observed spot price quotes and inear interpoation. This method does not attempt to predict changes in prices over time. The second approach augments the first by using market indicators to predict residua changes from the estimated price curve over time. This method expoits oca price stabiity in the short term by using the inear interpoation mode as a base, but sti aows for modeing price variabiity over time. The fina method appies regression to predict prices directy based on market indicators. This method aows for the greatest fexibiity in predicting price changes Linear interpoation price predictor As noted in many accounts of TAC/SCM agents, market prices in the game tend to exhibit oca price stabiity over short horizons. The degree of voatiity may vary depending on the particuar agents paying and random variations in the underying game state. However, there are structura reasons to expect such stabiity. One is that the underying suppier capacity and customer demand eves change over time, but rarey exhibit drastic changes over short time periods. In addition, the outstanding commitments and inventory of suppiers and manufacturers tend to exert a damping effect on component price changes. 14 We have found empiricay that the due dates for PC requests have minor effects on the price, so we do not mode these directy. Deep Maize estimates the current market state based on price quotes from recent days. We empoy inear interpoation to estimate prices for due dates with no recent observations. Fig. 7 shows an exampe price curve estimated using this method, which we term the inear interpoation price predictor (LIPP). Due to oca price stabiity, we expect LIPP to be a reasonaby good predictor for prices in the near future. Empirica resuts beow support this proposition Reative component price predictor In anayzing the performance of LIPP, we note a tendency for predictions over the entire price curve to systematicay overestimate or underestimate prices. There are severa pausibe reasons for this. Reca that suppiers current capacity varies according to a random wak during the game. Suppiers construct prices in part based on projecting their current production capacity into the future to determine their avaiabe capacity. Since avaiabe capacity is used in pricing for a request dates, fuctuations in capacity cause prices for a of these dates to rise or fa in unison. This pattern coud aso resut from manufacturing agents increasing or decreasing order quantities, but maintaining approximatey the same timing in their purchase schedues. This might resut, for instance, from rising or faing customer demand eves. LIPP does not take into account any information beyond recent price quotes that might hep to predict these sorts of price fuctuations. We introduce the reative component price predictor (RCPP) as a way of expoiting these additiona forms of information. RCPP predicts the residua error of LIPP by appying regression to technica attributes summarizing the observabe market state. A ist of the attributes we used is given in Tabe 3. The predictions made by RCPP are formed by cacuating the summation of the residua errors and LIPP predictions. The intuition for this approach is that the RCPP agorithm identifies game states that are ikey to resut in predictabe price shifts, eading to inaccurate LIPP estimates. The residuas modify the current price estimates to account for these shifts. This approach expoits the short-term accuracy of the inear price predictor, whie expoiting historica data and market indicators to adapt future forecasts. We note that there is a parae between this approach and the reative representation used in predicting prices in the PC market Absoute component price predictor The fina cass of predictors we consider is the absoute component price predictor (ACPP). ACPP appies regression to directy earn prices from the technica indicators. Unike RCPP, this approach does not bootstrap the short-term accuracy of LIPP, so it

10 72 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) Tabe 3 Attributes considered by RCPP and their RReiefF vaues for current and future days. The first five attributes correspond to parameters of an individua RFQ and the remainder of market state. Attribute Current Future Description Day Current day Sent-day Day the RFQ wi be sent Due-day Day the RFQ wi be due Duration Due-day minus sent-day Quantity RFQ quantity Linear-price LIPP price prediction Nearest-price-point-diff Nearest known price point distance (days from due date) Days-since-data Days since due date had a price quote Market-capacity Last suppier capacity from market report Estimated-capacity Estimate of suppier capacity using market reports and trend Surpus Avaiabe capacity minus agent demand in recent period Aggregate-surpus Avaiabe capacity minus agent demand in tota Mean-demand Mean customer demand for component Mean-ow-demand Mean customer demand for ow-end components Mean-mid-demand Mean customer demand for mid-range components Mean-high-demand Mean customer demand for high-end components 5-Day-demand Customer demand for ast 5 days 20-Day-demand Customer demand for ast 20 days 40-Day-demand Customer demand for ast 40 days is not reative to the estimated current prices. The potentia advantage of this approach is that it offers greater fexibiity for modeing price shifts, since it is not constrained by the LIPP prediction. If there are prevaiing ong-term price trends not captured in the RCPP residuas, ACPP may yied more accurate predictions at ong horizons. We note that there is a parae between this approach and the absoute representation used in predicting prices in the PC market. 7. Evauation of component market predictions We evauate the reative performance of the three casses of predictors on the basis of prediction error using the Prediction Chaenge framework. We present the resuts of experiments run after the competition using the data set from the fina round of the 2007 Prediction Chaenge. 15 The data consists of a tota of 48 games containing the designated PAgent, divided into three sets of 16 games payed against the same set of opponents. A opponents were seected from the agent repository. The predictors are scored using normaized RMS error on a required component price predictions Setting expiration intervas for LIPP We begin by exporing an important parameter of the LIPP method, which we then fix for subsequent anaysis. Reca that manufacturers are imited in the number of RFQs they may submit each day. We can increase the number of observations avaiabe for estimating the price curve by incuding RFQ responses from previous days, with the caveat that these quotes may represent stae information. We represent this tradeoff using an expiration interva that determines how many days of previous observations are used to construct the LIPP estimate. Using a onger interva increases the amount of data avaiabe, aong with the risk that the data no onger accuratey refects the current situation. To determine the best setting of the expiration interva, we tested intervas from one to five days. The resuts are shown in Fig. 8. The mean accuracy of the LIPP predictions decreases monotonicay as the size of the ength of the expiration interva is increased. This resut impies that the day-to-day price voatiity in 15 Many of these anayses were aso performed before the Chaenge using other test sets; we repeat a of the experiments using this data set for consistency. RMS Error EX1 EX2 EX3 EX4 EX5 Expiration Interva Fig. 8. RMS error for LIPP with various expiration intervas. TAC/SCM is high enough that the benefit of having data points for additiona due dates is outweighed by the reduced accuracy of the oder data points. It is possibe that adapting this expiration interva dynamicay during a game based on observed price voatiity or other factors coud yied more accurate predictions, but we have not yet fuy expored this possibiity Estimating attribute quaity for regression modes As a preiminary step to regression, we seek to evauate the quaity of various attributes that may be used to predict current and future component prices. Unike cassification probems, there are few measures of attribute quaity avaiabe from the current iterature. For exampe, information gain, j-measure, and v 2 cannot be used for estimating attribute quaity in a regression. Three measures that have been proposed for regression with numerica attributes are mean absoute and mean squared error (Breiman et a., 1984), and RReiefF (Robnik-Šikonja and Kononenko, 1997). Because the error measures assume independence among attributes, they are ess appropriate given strong interdependencies ike those introduced in our anaysis. In contrast, RReiefF has be shown empiricay to perform we in situations where there are strong interdependencies, such as parity probems. A short expanation of the RReiefF vaues is rather eusive (see reated work Robnik- Šikonja and Kononenko, 2003 for a thorough exposition), but we attempt here to give some intuition as to what the vaues represent.

11 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) RReiefF is an extension of the ReiefF agorithm to regression. In cassification, ReiefF measures an attribute s quaity according to how we a given attribute distinguishes instances that are simiar in the attribute space. The vaue itsef is the approximated difference of two probabiities with respect to a given attribute vaue. The first is the probabiity that a different vaue is observed given near instances from different casses. The second is the probabiity that a different vaue is observed given near instances from the same cass. Because price predictions and, in genera, regressions are continuous, we cannot cacuate these probabiities. RReiefF attempts to sove this probem by introducing a probabiity distribution which determines whether two instances are different. The vaues cacuated by RReiefF ie in the range [ 1, 1] with random attributes tending to be sighty negative. At the extremes, a vaue of near one signifies that a different attribute vaue impies a different regression vaue for nearby instances. A RReiefF vaue greater than zero indicates that the first probabiity subsumes the second and thus the attribute is ikey to discriminate nearby instances to a usefu extent. We adopt this simpe threshod to determine whether attributes are incuded in our regression modes. Our experience is consistent with the empirica findings that RReiefF attribute seection improves our regression modes over the defaut mode that incudes a avaiabe attributes. A compete ist of a attributes considered for regression anaysis as we as the RReiefF vaues for each attribute on both current and future day predictions is given in Tabe 3. The attributes are a mix of RFQ parameters and estimated market state. Note that RReiefF vaues often differ significanty with respect to current and future predictions. In particuar, the tabe suggests that current predictions are best determined by the attribute subset quantity, due-day, duration, and inear-price, a but the ast of which are RFQ parameter attributes. This differs notaby from future predictions, for which the majority of attributes are sti of threshod quaity. Component prices vary oosey according to a few market state parameters that are hidden from direct observation. Our attribute set was chosen in an attempt to extract usefu observabe parameters from the market in ieu of the hidden state. For current predictions, it appears that the market state attributes are not very usefu in regression. This is ikey expained by the observation that the interna market state changes graduay and that usefu portions of the interna state are aready expressed in the LIPP prices from the prior day. Thus, current prices can best be determined by attributes from the RFQ and LIPP prices, whereas incuding the estimates of market state is not beneficia. This is not to say that estimating interna market state is without predictive power in a cases. As the RRefiefF vaues in the future coumn suggest, the future market state is no onger refected in LIPP prices and incuding these attributes is ikey beneficia Comparing regression methods for RCPP There are many machine earning agorithms that coud be appied to earn the residua errors for RCPP. We tested a variety of regression agorithms from the Weka machine earning package (Witten and Frank, 2005) for this task, incuding inear regression, k-nn, support vector machines, and various decision-tree regressions. We generated training data from approximatey 50 game instances simuated on a oca computing custer. Each game of training data had one PAgent paying, aong with a coection of other agents taken from the agent repository (the same set of potentia opponents used for the Prediction Chaenge). Each game contains approximatey 1800 sampe price predictions for each CPU component and twice as many for non-cpu components. We train separate predictors for each component type, so we have approximatey 90,000 data points for CPU components and 180,000 for non-cpu components. We take sampes from the viewpoint of the PAgent in the training games, so the market indicators are computed with respect to this agent s observations. After some preiminary experimentation, we seected additive regression 16 and reduced-error pruning trees (REP trees) as the most promising candidates. Many of the other agorithms had simiar resuts in terms of prediction error, but required much onger to train or generated very arge modes. For some of the agorithms, overfitting was a severe probem. We tested severa parameter settings for both additive regression and REP trees using the data set from the fina round of the Prediction Chaenge. Additive regression was tested both with defaut settings and with a shrinkage rate of 10%. 17 REP Trees were tested with maximum tree depths of four through seven. A variations earned residuas from LIPP predictions with an expiration interva of one (the best setting from the previous section). Fig. 9 shows the prediction error resuts for these methods on both current and future predictions. The different earning agorithms produced very simiar resuts; each woud have paced first in both component prediction categories. For the actua chaenge, we used the REP tree agorithm with maximum depth five to earn residuas for RCPP, since this agorithm was consistenty accurate for both current and future predictions Comparison of prediction methods In the previous sections, we expored variations of the LIPP and RCPP methods to identify good parameter settings for these agorithms. We now directy compare the performance of the three different casses of methods introduced in Section 6. We use the LIPP method with expiration interva one, the RCPP method earning residuas using REP trees of max depth five, and an ACPP predictor that uses additive regression to make price predictions directy from the technica indicators. 18 Prediction error resuts for a three agorithms on both current and future predictions are given in Fig. 10. A current comparisons in the figure are statisticay significant beyond the eve and a future comparisons in the figure are statisticay significant beyond the 0.05 eve using a standard t- test. For the current price predictions, the performance for LIPP and RCPP is very cose, with both outperforming the absoute predictor by a wide margin. This is strong evidence that the LIPP method effectivey summarizes the current price state, and that this is a very good predictor of prices in the near future due to oca price stabiity. Interestingy, none of the methods we tried for earning residuas were abe to improve LIPP predictions by a significant margin. This suggests that in the near term, most of the information about market conditions is effectivey summarized by the current prices. The benefits of earning prices from historica data using technica indicators is evident in the resuts for predicting future prices. Both ACPP and RCPP perform better than the LIPP method in this case, demonstrating the vaue of representing changes in prices over time. RCPP performs better than ACPP on these future predictions, indicating that the current prices sti have significant predictive vaue, even at a 20-day horizon. Overa, the RCPP method, which combines the price estimates from inear interpoation with earned residuas, offers the best of both words; it retains shortterm accuracy whie significanty improving ong-term forecasts. 16 Additive regression is a meta-earning agorithm wherein each decision stump is fit to the residua of the previous step every iteration. 17 The shrinkage rate considers how much of the trained decision stump is used each iteration. Normay, the shrinkage rate is set to 100%, however, a smaer shrinkage rate induces a smoothing effect and reduces overfitting. 18 Based on the resuts in the previous section, we woud expect a REP-tree version of ACPP to have very simiar performance.

12 74 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) Current RMS Error Future RMS Error AddReg Shrink REP4 REP5 REP6 REP7 Predictor AddReg Shrink REP4 REP5 REP6 REP7 Predictor Fig. 9. Prediction error resuts for various candidate earning agorithms on the data set from the fina round of the Prediction Chaenge. Future corresponds to a 20-day horizon. Current RMS Error Future RMS Error ACPP RCPP LIPP Predictor ACPP RCPP LIPP Predictor Fig. 10. Prediction errors for the absoute (ACPP), reative (RCPP), and spot (LIPP) predictors on the Prediction Chaenge fina round data set. Future corresponds to a 20-day horizon. We seected RCPP for use in both the Prediction Chaenge and the main tournament Suppy chain performance In this section, we anayze the effects of component prediction methods on aggregate agent performance, simiar to the anaysis performed on the customer prediction effects described in Section 5.2. We ran simuations using a profie of TacTex-07-Finas, Phant- Agent-07, Mertacor-05, MinneTAC-06, and two versions of Deep Maize. One version of Deep Maize stayed static and was used as the baseine agent. In this case, the baseine agent was Deep-Maize-07-Finas, which used RCPP with LIPP5 for its component predictions. The second Deep Maize agent competing in the simuations used either LIPP1, ACPP, or RCPP with LIPP1 for its component predictions. To evauate each regression method, we ran three sets of games, invoving no ess than 35 games in each set. We report the difference in score between the variation of the baseine using the indicated predictor and the baseine itsef, as we as the p-vaue of the corresponding paired t-test. We found a pairwise comparisons to be significanty different at a eve beyond The resuts are presented in Tabe 4. We expect that the reative performance of each variation of Deep Maize wi correspond to the accuracy of the prediction method used by the agent. The resuts support this for current price predictions, but show ess sensitivity to the accuracy of ong-term predictions. The predictor which fared the best in the prior section, RCPP with LIPP1, was an $0.8 M improvement over the baseine agent, with the ony difference being an expiration interva of Tabe 4 Reative score with respect to the baseine agent in simuated games. The numbers represent the difference between two versions of Deep Maize, one using the indicated predictor and the other using the version payed in the 2007 tournament finas (Deep- Maize-07-Finas). In addition the p-vaue of each paired t-test is shown. Predictor Reative score p-vaue RCPP with LIPP M ACPP M <2.2e-16 LIPP M one versus five in LIPP. Averaged over a arge number of games, this is a substantia difference in a profie of competitive agents. Surprisingy, LIPP1 without RCPP was aso an improvement over the baseine agent. This is interesting because LIPP1 predicts future prices simpy using its current prediction with no adjustment. Thus, Deep Maize was abe to perform quite we without making an effort to adjust for future component prices. This effect is aso evident in the resut for the ACPP version. In the prior section, we noted that athough ACPP performed poory in current predictions, it fared we in future predictions when compared to LIPP. The poor performance in the current prices had drastic consequences for the overa agent score. The effect of the arge errors in current prices caused Deep Maize to procure far fewer components and thus caim ess PC market share, which exacerbated the reative score difference by opening up more profitabe market share to the other agents. A three tests support the proposition that prediction accuracy exerts a noticeabe effect on an agent s performance, especiay when evauating current price predictions.

13 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) TAC/SCM tournament and prediction chaenge The TAC/SCM tournament and Prediction Chaenge offer distinct opportunities for evauation of our prediction methods in comparison with aternatives outside our contro. The Prediction Chaenge faciitates direct comparisons with competing prediction approaches, isoating this aspect of the game. The genera tournament resuts aow us to evauate the genera competency of our agent reative to the other competitors. Predictions are an important component of Deep Maize s decision-making, so the overa performance of the agent refects in part the quaity of these predictions. An important aspect of both the SCM tournament and the Prediction Chaenge is that each new game instance may present nove strategic environments not be refected in any historica data. Thus, this exercise serves as an important indication of the robustness of our prediction resuts TAC/SCM tournaments Tournament performance is an important indicator of the overa competence of TAC/SCM agents. Each TAC/SCM tournament comprises a sequence of rounds: quaifying, seeding, quarter-finas, semi-finas and finas. The quaifying and seeding rounds span severa days and are used primariy for deveopment and testing. The quarter-finas, semi-finas and finas are hed on successive days. In 2005 and 2006, 24 agents were seected to begin the quarter-finas, with haf eiminated in each round. In 2007, 18 agents started the quarter-finas, with six eiminated in each round. Resuts from the 2005, 2006 and 2007 tournament semi-fina and fina rounds incuding Deep Maize are presented in Tabes Deep Maize has performed very we in each of the TAC/SCM tournaments to date. Our agent reached the fina round each year, pacing fourth in 2005, third in 2006 and third in Deep Maize aso demonstrated strong performance in the semi-fina rounds, pacing first in each heat. This record of overa performance provides evidence that Deep Maize is effective in a wide variety of competitive environments. The version of the customer prediction modue presented here is very simiar to the modues that payed in a the tournaments. This aspect of the agent was argey unmodified between 2005 and 2007, though other eements of the agent underwent significant revisions. In 2005 and 2006, Deep Maize used ony LIPP5 for component market predictions. RCPP was added to the predictions for the 2007 tournament (using a REP Tree with a maximum depth five), however we sti maintained an expiration interva of five for LIPP. Unfortunatey, we did not discover the superior accuracy of ower expiration intervas unti shorty before the finas, such that we coud not make the modification and competey test the strategy. The training data used for 2007 tournament pay was derived from approximatey 100 game instances, incuding games from the ate rounds of the 2006 tournament and additiona simuations using the best avaiabe agents from the agent repository TAC/SCM 2007 Prediction Chaenge The introduction of the Prediction Chaenge aows us to directy compare our prediction approaches to other competitors, suppementing our own anaysis based on controed experiments. The Prediction Chaenge was payed in two rounds, a semi-fina and a fina. The semi-fina round took pace during the same time-frame as the TAC/SCM seeding round, before the main tournament. Like the quaifiers and seeding rounds in the main TAC/ 19 More detais about the tournament structure and fu resuts are avaiabe at the TAC web site, Tabe 5 Scores and rankings from the rounds Deep Maize payed in during the 2005 SCM tournament. A scores are in miions of doars. The adjusted coumn eiminates two game instances (3718 and 4259) where the University of Michigan network ost connectivity during the game, distorting the resuts substantiay. Semi-Finas 2 Finas Finas (adjusted) Deep Maize 3.68 TacTex TacTex TacTex SouthamptonSCM 1.60 Deep Maize 2.06 MinneTAC 2.27 Mertacor 0.55 SouthamptonSCM 1.55 RationaSCM 2.28 Deep Maize 0.22 Mertacor 0.53 CMieux 2.33 MinneTAC 0.31 MinneTAC 0.33 PhantAgent 6.64 Maxon 1.99 Maxon 1.74 Tabe 6 Scores and rankings from the rounds Deep Maize payed in during the 2006 SCM tournament. A scores are in miions of doars. Semi-finas 2 Finas Deep Maize 6.45 TacTex Maxon 4.08 PhantAgent 4.15 Botticei 1.95 Deep Maize 3.58 CMieux 1.81 Maxon 1.75 SouthamptonSCM 1.63 Botticei 0.48 Mertacor 1.44 MinneTAC 2.70 Tabe 7 Scores and rankings from the rounds Deep Maize payed in during the 2007 SCM tournament. A scores are in miions of doars. Semi-Finas 1 Finas Deep Maize 9.76 PhantAgent 8.67 Tinhorn 6.94 TacTex 6.31 Maxon 5.63 DeepMaize 5.45 MasterBham 5.40 Maxon 1.79 CrocodieAgent 5.12 Tinhorn 1.34 Sorter CMieux 1.24 SCM tournament, this round was meant as a preiminary test of the overa Prediction Chaenge for both the organizers and competitors. The fina round took pace the day before the main TAC/ SCM finas. In both rounds, every competitor was given eight hours to make predictions about the 48 games defining the round. Competitors were aowed to produce their predictions any time during this period, independenty of the other competitors. The resuts from the Chaenge semi-finas and finas are shown in Tabe 8. Deep Maize paced first overa in the finas, achieving the top score in both component prediction categories and the secondbest scores in both PC prediction categories. These resuts provide Tabe 8 TAC/SCM Prediction Chaenge 2007 Resuts (RMS error normaized by base price). Prediction Agent Semi-finas Finas Current PCs TacTex Deep Maize Botticei Kshitij Future PCs TacTex Deep Maize Botticei Kshitij Current components Deep Maize Botticei TacTex Kshitij Future components Deep Maize Botticei TacTex Kshitij

14 76 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) additiona support for the overa efficacy of our methods. Deep Maize used a variation of RCPP for the semi-fina round of the Prediction Chaenge. Among other differences, this version used an expiration interva of five for the inear price interpoations. The fina round version used an expiration interva of one, which argey account for the significant improvement in current component price predictions between the semi-fina and fina round. The data set for component price predictions was based on games specificay simuated for the Prediction Chaenge, as discussed in Section 7.3. The customer price predictor used in the Chaenge was identica to the version used by Deep Maize in the 2006 TAC/SCM tournament, incuding the data set. 9. Concusions We document and anayze successfu approaches for forecasting prices in a chaenging market domain. The genera principe of our design is to support expoitation of a possibe sources of information. To this end, we integrate severa we-known ideas in an nove way, resuting in better overa predictions. In the PC market, we evauate our ideas against a baseine predictor simiar to those used by many competing agents, appying both error measures and simuation performance as benchmarks. We show that improved predictions can dramaticay improve agent performance in TAC/SCM. This is particuary interesting in ight of the substantia uncertainties inherent in the domain and chaenges of predicting the behavior of other agents. The technique we present for appying transformations to predictions using onine scoring is particuary interesting, and shoud be appicabe in many domains. This method provides a way to perform principed combinations of predictions based on different sources of data, as we as a way to reduce systematic errors. It does these by making use of additiona information derived from onine performance. This method showed consistent benefits in our experiments across a range of conditions on both prediction error and simuation performance metrics. We aso investigated the use of absoute and reative representations for predictions. It appears that each of these representations has advantages under certain conditions, particuary reated to how the information is used in decision-making. In the component market we deveop methods to integrate voatie spot price predictions with a ong-term predictor using mutipe sources of inter-market information. This reative predictor is more accurate than either the spot predictions or absoute price predictions from historica data in isoation. Our prediction methods for both markets demonstrate strong overa performance, demonstrated in interna experiments and in our first-pace finish in the inaugura TAC/SCM Prediction Chaenge. These predictions have aso contributed to the strong overa performance of Deep Maize in the TAC/SCM tournament in recent years. Acknowedgements Thanks to the participants and organizers of the TAC/SCM competition for providing such a fruitfu research environment. We owe particuar gratitude to David Pardoe for designing and operating the Prediction Chaenge. Kevin O Maey contributed to the Deep Maize infrastructure. This work was supported in part by NSF grant IIS , and the STIET program under NSF IGERT grant References Bates JM, Granger CWJ. The combination of forecasts. Oper Res 1969;20(4): Benisch M, Greenwad A, Naroditskiy V, Tschantz M. A stochastic programming approach to scheduing in TAC SCM. In: Fifth ACM conference on eectronic commerce. New York; p Benisch M, Sardinha A, Andrews J, Sadeh N. CMieux: Adaptive strategies for competitive suppy chain trading. In: Eighth internationa conference on eectronic commerce. Ann Arbor; p Breiman L, Friedman J, Stone CJ, Oshen R. Cassification and regression trees. Chapman & Ha/CRC; Brockwe PJ, Davis RA. Introduction to time series and forecasting. Springer- Verag; Brooks CH, Gazzae R, Das R, Kephart JO, MacKie-Mason JK, Durfee EH. Mode seection in an information economy: Choosing what to earn. Comput Inte Burke DA, Brown KN, Hnich B, Tarim A. Learning market prices for a rea-time suppy chain management trading agent. In: AAMAS-06 workshop on trading agent design and anaysis. Hakodate; Chatfied C. Time-series forecasting. Chapman & Ha/CRC; Cheng S-F, Leung E, Lochner KM, O Maey K, Reeves DM, Weman MP. Waverine: A Warasian trading agent. Decis Support Syst 2005;39: Cemen RT, Winker RL. Combining probabiity distributions from experts in risk anaysis. Risk Ana 1999;19(2): Coins J, Arunachaam R, Sadeh N, Eriksson J, Finne N, Janson S. The suppy chain management game for the 2007 Trading Agent Competition. In: Technica report CMU-ISRI Carnegie Meon University; Eriksson J, Finne N, Janson S. Evoution of a suppy chain management game for the Trading Agent Competition. AI Commun 2006;9:1 12. Ghani R. Price prediction and insurance for onine auctions. In: Internationa conference on knowedge discovery in data mining; p Hanson R. Combinatoria information market design. Inform Syst Front 2003;5(1): Hastie T, Tibshirani R, Friedman J. Eements of statistica earning. Springer- Verag; He M, Rogers A, Luo X, Jennings NR. Designing a successfu trading agent for suppy chain management. In: Fifth internationa joint conference on autonomous agents and mutiagent systems. Hakodate; p Jordan PR, Kiekintved C, Weman MP. Empirica game-theoretic anaysis of the TAC suppy chain game. In: Sixth internationa joint conference on autonomous agents and mutiagent systems; p Kaufman PJ. Trading systems and methods. third ed. John Wiey and Sons; Keer PW, Duguay F-O, Precup D. RedAgent-2003: an autonomous market-based suppy-chain management agent. In: Third internationa conference on autonomous agents and mutiagent systems; p Ketter W. Identification and prediction of economic regimes to guide decision making in muti-agent marketpaces. PhD thesis, University of Minnesota; January Ketter W, Coins J, Gini ML, Gupta A, Schrater P. A predictive empirica mode for pricing and resource aocation decisions. In: Ninth internationa conference on eectronic commerce. Minneapois; p Kiekintved C, Weman MP, Singh S, Estee J, Vorobeychik Y, Soni V, Rudary M. Distributed feedback contro for decision making on suppy chains. In: Fourteenth internationa conference on automated panning and scheduing. Whister, BC; p Kiekintved C, Vorobeychik Y, Weman MP. An anaysis of the 2004 suppy chain management trading agent competition. In: IJCAI-05 workshop on trading agent design and anaysis. Edinburgh; Kiekintved C, Mier J, Jordan PR, Weman MP. Controing a suppy chain agent using vaue-based decomposition. In: Seventh ACM conference on eectronic commerce. Ann Arbor; p Kiekintved C, Mier J, Jordan PR, Weman MP. Forecasting market prices in a suppy chain game. In: Sixth internationa joint conference on autonomous agents and mutiagent systems; p Nogaes FJ, Contreras J, Conejo AJ, Espinoa R. Forecasting next-day eectricity prices by time series modes. IEEE Trans Power Syst 2002;17: Osepayshvii A, Weman MP, Reeves DM, MacKie-Mason JK. Sef-confirming price prediction for bidding in simutaneous ascending auctions. In: Twenty-first conference on uncertainty in artificia inteigence. Edinburgh; 2005; p Pardoe D. The TAC SCM prediction chaenge. 2007; < edu/tactex/predictionchaenge/>. Pardoe D, Stone P. Bidding for customer orders in TAC SCM. In: Agent mediated eectronic commerce VI, ecture notes in artificia inteigence, vo Springer; Pardoe D, Stone P. TacTex-05: A champion suppy chain management agent. In: Twenty-first nationa conference on artificia inteigence. Boston; p Pardoe D, Stone P. Adapting price predictions in TAC SCM. In: AAMAS-07 workshop on agent mediated eectronic commerce IX. Honouu; 2007a. Pardoe D, Stone P. An autonomous agent for suppy chain management. In: Adomavicius G, Gupta A, editors. Handbooks in information systems series: business computing. Esevier; 2007b. Pindyck RS, Rubinfed DL. Econometric modes and econometric forecasts. 4th ed. Irwin/McGraw-Hi; Robnik-Šikonja M, Kononenko I. An adaptation of reief for attribute estimation in regression. In: Fourteenth internationa conference on machine earning. Nashvie; p Robnik-Šikonja M, Kononenko I. Theoretica and empirica anaysis of ReiefF and RReiefF. Mach Learn 2003;53:23 69.

15 C. Kiekintved et a. / Eectronic Commerce Research and Appications 8 (2009) Stone P, Schapire RE, Littman ML, Csirik JA, McAester D. Decision-theoretic bidding based on earned density modes in simutaneous, interacting auctions. J Artif Inte Res 2003;19: Weman MP, Reeves DM, Lochner KM, Vorobeychik Y. Price prediction in a trading agent competition. J Artif Inte Res 2004;21: Weman MP, Greenwad A, Stone P. Autonomous bidding agents: strategies and essons from the trading agent competition. MIT Press; Witten IH, Frank E. Data mining: practica machine earning toos and techniques with Java impementations. Morgan Kaufmann; 2005.