A Novel Auction Mechanism for Selling Time-Sensitive E-Services

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1 A ovel Aucton Mechansm for Sellng Tme-Senstve E-Servces Juong-Sk Lee and Boleslaw K. Szymansk Optmaret Inc. and Department of Computer Scence Rensselaer Polytechnc Insttute th Street, Troy, Y 12180, USA {leej6, Abstract Many e-servces are tme-senstve as the users request them for a specfc tme perod. Such servces need to be repeatedly offered to keep them constantly utlzed. Ths paper studes wnner selecton strateges n a recurrng aucton for such tme-senstve e-servces. We observe that because of uneven wealth dstrbuton, the least wealthy bdders tend to drop out of recurrng aucton as they persstently loose. The bdders droppng out of an aucton decrease competton and can cause a collapse of wnnng prces. We propose and evaluate a novel aucton mechansm that enables bdder drop control. Compared to tradtonal aucton mechansms, ours ncreases revenue of the e-servce provder and decreases loss of farness of the e-servce allocaton. 1. Introducton E-servce s a modular, nmble, Internet-based servce that most often requres varous tme senstve system resources such as bandwdth, computatonal power or memory to guarantee the Qualty of Servce (QoS) to accomplsh ther tasks. Thus, e-servces often have tme-senstve property 1. Such e-servces, f not used for a certan tme perod, persh, as they cannot be stored n the warehouse for a future use. Moreover, tme-senstve e-servces have to be offered for sale repeatedly to keep them beng utlzed all the tme. Increasng domnance of servce-orented paradgm n the overall U.S. economy underscores the mportance of e-servces and ts mportant aspect, effcent prcng. In many exstng electronc markets, fxed prcng or statc tme-dfferental prcng mechansms are wdely used because of ther smplcty. However, there s a natural varaton n customer s demand over tme. For ths reason, those prcng mechansms are nsuffcent. They lead to under-utlzaton of tme-senstve 1 Examples of ths type of e-servces are varous Grd Computng Servces, ncludng utlty computng, and Internet based multmeda servces such as Vdeo On Demand (VOD), Vdeo Conferencng, Musc on Demand, and so on. resources when demand s low and under-prcng when demand s hgh. In a statc tme dfferental prcng mechansm two or more ters of on/off peak rates can mprove effcency by partal matchng of lower demand wth lower prce. However, ths mechansm stll remans nflexble, snce demands of customers do not follow a step functon, but they shft rather gradually from on- to off-peaks. A contnuously adjustable dynamc prcng mechansm that adapts to changng market condtons s more effcent. It can maxmze both tme-senstve resource utlzaton and revenue n a varety of market condtons. Durng the low utlzaton perod, the low prce nvoked by the adaptve prcng can ncrease competton. Durng the hgh demand perod, emergng hgh prces ncrease the servce provder revenue. Moreover, wth such a mechansm, the prce tself becomes an mportant sgnal for controllng far allocaton of resources. However, ths very dynamsm of prcng makes the servce provder s prcng decsons dffcult. An aucton mechansm can mtgate ths dffculty. In electronc market envronments, use of an aucton provdes the several benefts. (1) Auctons are nherently easy to understand by both customers and the servce provder. (2) Rules and procedures that defne an aucton are usually easy to mplement n automated electronc envronments [3]. (3) An aucton elmnates any need for defnng complex dynamc prcng structures. (4) Auctons support decentralzed prcng and therefore avod abusve market practces [6]. An aucton for tme senstve e-servces s n fact a recurrng aucton, as the traded e-servces must be repeatedly resold for future tme perods. Applyng tradtonal aucton mechansms, such as Englsh or Vckery ones [7], to such an aucton may result n an nevtable starvaton for resources for certan customers. As a result, the affected customers may decde to drop out of the future aucton rounds, thereby decreasng the long-term demand for e-servces. The

2 lowered demand may lead to the collapse of the value of the bds needed to wn an aucton round. In such a development, the e-servce provder cannot guarantee the revenues above ts mnmum cost. To stablze revenue, the e-servce provder must prevent the prce collapse and that requres mechansms to control the resource supply and the bdder drop problem. In ths paper, we propose a novel aucton mechansm, called the Optmal Recurrng Aucton (ORA), for the repeatedly requested tme-senstve e-servces. Ths mechansm focuses on reducng the bdder drop problem, elmnatng the resource waste and avodng an asymmetry of the negotaton power from whch the tradtonal aucton mechansms suffer. The proposed mechansm s applcable to a multple wnner, dscrmnatory prcng, and sealed bd aucton wth the seller reservaton prce. The mechansm attempts to mnmze the communcaton overhead and to maxmze the seller s revenue. The remnder of ths paper s organzed as follows. In the next secton, we brefly descrbe prevous approaches to maxmzng the seller s revenue n an aucton mechansm desgn, analyze potental market envronments for e-servces and defne the problems that motvate our work. Secton 3 llustrates the novel aucton mechansm ORA. The proposed mechansm s verfed by varous experments whose results are gven n Secton 4. Fnally, n Secton 5, summares of the contrbutons and future works are ncluded 2. Related Works 2.1 Seller s Optmal Aucton Mechansms The two man approaches proposed prevously to maxmze the seller s revenue are based on controllng the resource supply and named the guaranteed market clearng prce approach and the guaranteed revenue approach. They are often referred to as seller s optmal aucton mechansms [3]. In the guaranteed market clearng prce approach, only the bdders bddng hgher than the reservaton prce of the auctoneer (or seller) are wnners [4]. In ths case, the auctoneer may sell only a part of the entre stock, f ths s what s needed to servce the wnners. In the guaranteed revenue approach, f the revenue that emerges from the wnners bddng dose not meet the expectatons of the auctoneer, the entre aucton s canceled [5]. Ths means that n each aucton round the auctoneer ether sells ts entre stock or none at all. In ths paper, we refer to those mechansms as Reservaton Prce Aucton (RPA) and Cancelable Aucton (CA), respectvely. 2.2 Potental Market Envronments Dfferent market structures requre dfferent prcng and negotaton mechansm [3]. Hence, precse analyss of market envronments s one of the essental steps n the desgn of an effcent aucton-based dynamc prcng and negotaton mechansm. We assume that there are many customers and one e- servce provder n the market. Multple unts of premum-qualty, homogeneous e-servces are traded. Those e-servces requre certan amount of predefned tme-senstve resources to guarantee the servce premum qualty. The customers request repeatedly the desred e-servces for a certan (each tme dfferent) tme nterval. After the requested tme perod ends, the allocated tme-senstve resource becomes free and need to be offered to customers agan. Hence, an aucton n such a market s a recurrng one. Each customer s true valuaton (.e., her wllngness to pay) s restrcted by her wealth that s unevenly dstrbuted among customers. We make the followng assumptons: the true valuaton of each customer s ndependently dstrbuted (so-called an Independent Prvate Value Model assumpton); each customer keeps hs true valuaton constant; customers are rsk neutral and symmetrc. From the assumpton of a rsk neutral customer and perfectly sealed bds, t follows that each customer bds the prce b that maxmzes hs expected payoff (.e., utlty), U ( b) defned as U ( b) = ( t b) q( b), (1) where t denotes true valuaton of customer and q( b) denotes the probablty of wnnng wth the bddng prce b. There s a trade-off relatonshp between the proft factor (.e., t b ) and the wnnng probablty, q( b ). If the customer bds more, the wnnng probablty rses, but the resultng proft factor decreases. Conversely, f the customer bds less, the proft factor ncreases at the expense of the wnnng probablty. Lkewse, n a recurrng aucton, f a customer lost n the last aucton round, she may ncrease her bd n the current round to ncrease the wnnng probablty. If a customer won n the last round, he may mantan the bddng prce or decrease t n the current round to ncrease the proft factor. 2.3 Motvatons for ovel Aucton Mechansm The tradtonal auctons, ncludng the seller s optmal auctons, when appled to the tme-senstve e-servces, cause the followng three problems.

3 1) Asymmetrc balance of negotatng power: In most of the tradtonal aucton mechansms, the prces bd n an aucton are dependent only on the customer s wllngness to pay for the traded goods. Ths means that ntentons of only customers, but not the e-servce provder, are reflected n the aucton wnnng prces. 2) Resource waste: To restore the symmetrc balance of negotatng power, the seller s optmal aucton mechansms such as RPA and CA, were proposed [4, 5]. However, when the tme-senstve resources are traded, the seller s optmal auctons cause resource waste. In RPA, the reservaton prce restrcts the number of wnners. In CA, the cancellaton of an aucton round wastes the entre stock of resources. Our expermental results presented n Fgure 1 show the extent of the resource waste n RPA and CA % of resources n RPA and 23.5% of resources n CPA are wasted n the market envronments of the experments descrbed n Secton 4.1. Fgure 1. The Resource Waste Problem 3) Bdder drop problem: Prces bd n an aucton are dependent on the wllngness of each customer to pay. Ths wllngness n turn can be expressed as the customer true valuaton. Each customer s wealth nfluences the upper bound on the customer s wllngness to pay. An uneven wealth dstrbuton can cause starvaton of poor customers n a recurrng aucton. A frequent starvaton for the traded resources (.e., e-servces n many e-markets) decreases the customer s nterest n the future aucton rounds. In such a stuaton, f some customers conclude that t s mpossble or unlkely that they wll wn at the prce that they are wllng to pay, they wll drop from the future aucton rounds. In a recurrng aucton, each customer s drop out of an aucton decreases the number of actve customers. We wll refer to actve customers as bdders. Such a drop n the number of bdders gradually decreases the prce competton. In the long run, when the number of bdders drops below a certan level, the seller can not guarantee the expected revenues n the future aucton rounds. Ths s because the remanng bdders constantly wn and as a result they may decrease ther bddng prces for future aucton rounds to maxmze ther expected proft. Thus, n such a scenaro, the bddng prce guaranteeng the wn n an aucton round may collapse to a very low level. The mportance of bdder drop control (.e., mantanng prce competton) 2 s proved theoretcally n our recent studes [9, 10]. The Fgure 2 shows the drect effect of the bdder drop problem on the revenue of the e- servce provder based on the expermental scenaros descrbed n Secton 4.1. Fgure 2. The Bdder Drop Problem 3. Optmal Recurrng Aucton Mechansm The bdder drop problem n a recurrng aucton for the tme-senstve e-servces s the man reason of the revenue nstablty resultng from the prce collapse. To prevent such nstablty, we propose an Optmal Recurrng Aucton (ORA) mechansm that focuses on reducng the bdder drop problem, elmnatng the waste of resources, and restorng symmetry of the negotatng power. The man dea of the mechansm s based on the demand-supply prncple of mcro-economcs [1]. As shown n Fgure 3, when demand falls from D1 to D2 durng a recurrng aucton, the mnmum marketclearng prce decreases from p1 to p2. In ths case, to mantan or ncrease the mnmum market-clearng prce to p1, seller (.e, auctoneer) must decrease the supply of resources from q1 to q2 (.e., the entre supply curve needs to change from S1 to S2). Conversely, when the overall bd prce ncreases, the seller may ncrease the supply. When sellng e-servce, however, f the seller decreases the supply for a gven tme perod, the unsold resources are wasted. In contrast, n the proposed mechansm, the unsold resources (q1 q2 n Fgure 3) are sold to the bdders who have hgh probablty of droppng out of the forthcomng aucton round. Ths soluton reduces the 2 In a Vckrey aucton, theoretcally, the optmal bddng prce s ndependent on the number of partcpants. Yet, Vckery notced n hs work [7] that when the competton s weak, the revenue may become small. Several other examples of smlar phenomena were found n the real world stuatons reported n [8]. Hence, the bdder drop control s also an mportant factor n Vckrey aucton.

4 bdder drop problem and keeps enough bdders nterested n an aucton to mantan the competton for resources. Smultaneously, usng unsold resources for bdder drop control resolves the resource waste problem. Prce p1 p2 D2 D1 S2 q2 S1 Fgure 3. The Demand-Supply Prncple q1 Quantty hgher than the reservaton prce of the e-servce provder and there are enough resources (.e., e-servce unts) to assgn one to all of them. The DL class conssts of customers who already dropped out of the aucton. The bdders who are n the WL class can be wnners or losers dependng on the bdder drop control mechansm appled. The numbers of bdders n the DW, WL and DL classes are denoted as dw, wl and dl, respectvely. Fgure 4 shows the bdder s classes n the ORA and compares them wth the classes n the tradtonal aucton mechansms. To descrbe the proposed ORA mechansm based on the above man dea, we defne here the fundamental notons of a bdder, bddng prce, and goods. Lower bddng prce TL Hgher bddng prce TW R Bdder: There are n + 1 bdders, denoted by = 0,..., n, ncludng n customers, = 1.. n, and the e- servce provder = 0. Each bdder reports hs bddng prce b0, b1, b2,..., b n n each aucton round. We assume the sealed bddng, thus only a bdder and the e-servce provder can communcate. Goods: There are R unts of tme-senstve resources that can be assgned to the homogeneous e-servce for the predefned tme perod. The e-servce provder trades these assgnments n each aucton round. Each bdder requres one unt of tme-senstve resources for the desred guaranteed premum-qualty e-servce. Thus, n ths paper, we regard tradng R unts of tmesenstve resources as tradng R unts of homogeneous premum qualty tme-senstve e-servces Bdder s Class Defnton The frst step of the ORA mechansm s to defne the bdders classes based on each bdder s bddng prce b, where = 1,..., n and the e-servce provder s reservaton prce b 0. The e-servce provder classfes the bdders nto the Defntely Wnner (DW), Wnner or Loser (WL) and Defntely Loser (DL) classes usng the followng condtons: DW f b & b0 r > n R, = 1, 2,..., n, DL f b 0, = 1, 2,..., n, (2) WL otherwse, where r denote rank of bdder n the ncreasng order of bddng prces of all customers. In each aucton round, the DW class bdders become wnners wthout any addtonal consderatons, snce they bd DL WL :Wnner :Loser WPWL DW Fgure 4. The Bdder s classes n the ORA In Fgure 4, TL and TW denote the Tradtonal Losers and Tradtonal Wnner classes as defned by the tradtonal aucton mechansm. WPWL represents the Wnnng Porton of the WL class, and the number of wnners n the WL class s denoted by wpwl. Hence, wpwl = R dw (3) The e-servce provder s bddng prce plays the same role as the reservaton prce of RPA. By ntroducng reservaton prce, the ORA mechansm creates symmetry n balance of the negotatng power from lack of whch the tradtonal aucton mechansms suffer. 3.2 Bdder Drop Control Mechansm By selectng wnners n the WL class, the ORA mechansm encourages them to stay n the aucton, so the wnners should nclude those bdders n the WL class who are consderng droppng out of the aucton. Thus, the mportant role of the bdder drop control s to select wnners n the WL class effcently. As the frst approxmaton of such a mechansm, we propose the Valuable Last Loser Frst Bdder Drop Control (VLLF-BDC) algorthm. The man dea behnd ths algorthm s to allocate the desred e-servce to a customer before she drops out of an aucton. The algorthm conssts of two phases. In the frst phase, the b 0

5 bdders who lost n the last aucton round but bd n the current round hgher prce than n the prevous one are marked as potental wnners. The marked bdders are ranked accordng to ther bddng prces and up to the wpwl hghest ranked marked bdders are selected as wnners of the current aucton round. If the number of the marked bdders s smaller than wpwl, the remanng resources are allocated n the second phase of the algorthm. The wnner selecton n the frst phase s nfluenced by the bds and wnnng record n the prevous aucton round, so there could be some loss of farness. To compensate for t, n the second phase, the hghest bddng unmarked bdders n the WL class are selected as wnners of the remanng resources. By markng only those last losers who bd hgher n the current round than n the prevous one, the algorthm prevents bdders wth low bddng patterns from becomng wnners. 3.3 Optmal Dstrbuton of Resources By usng a bdder drop control algorthm, the proposed ORA mechansm can mantan prce competton and therefore stablze the e-servce provder revenue durng the recurrng aucton. For these purpose, there should be resources reserved for the bdder drop control because allocatng all resources to the DW class would reduce the ORA to the tradtonal aucton wth all ts dsadvantages. Hence, for the bdder drop control to work effcently, the e-servce provder must use the optmal reservaton prce. After all, ths s the reservaton prce of e-servce that defnes the membershp n the DW class Optmal Range of Reservaton Prce Throughout ths paper, we defne C m as the mnmum cost of a unt of traded resources. The e-servce provder should set ths cost after consderng nternal and external expenses. Ths cost can also be nterpreted as the e-servce provder s desred mnmum prce for the unt of tme-senstve resources. The specfc mechansm for decdng C m s beyond the scope of ths paper. The mnmum revenue of an aucton round wth the bdder drop control should be larger than the e-servce provder s proftablty revenue. A suffcent condton to ensure ths constrant s b0 dw + Pwlmp ( R dw ) > Cm R, (4) where P wlmp represents the average bddng prce of wnners n the WL class. Hence Cm R b0 dw Pwlmp > R dw (5) To control bdder drop effcently, dw should be smaller than R to preserve some unts of tme-senstve resources for the bdder drop control. Hence, the followng condtons on dw, and P wlmp can be derved: 0 < R; 0< P < b (6) dw wlmp Usng nequaltes (4) and (6), the condton for the optmal reservaton prce values s b > C (7) 0 m Therefore, the e-servce provder should bd a hgher prce than the mnmum cost of a unt of tme-senstve resources to mantan proftablty of each aucton round. The upper bound of a range for the optmal reservaton prce s constraned by the nterrelatonshp between three types of customer s classes and farness. As shown n Table 1, an ncrease n the reservaton prce decreases the number of customers n the DW class (.e., dw decreases). Ths change results n an ncrease n the number of resource unts reserved for the bdder drop control. Thus, n ths case, the sze of the DL class decreases (.e., dl decreases). Snce decreasng dl means ncreasng prce compettons, the resultng total revenue of e-servce provder n the recurrng aucton usually ncreases (ths ncrease s the largest when dw = R and then t steadly shrnks and may become negatve for larger reservaton prces, when dw s smaller). However, ncreasng the number of the resource unts reserved for the bdder drop control decreases farness of resource allocaton. Ths s because the wnners n the frst phase of the VLLF algorthm are selected based not only on ther current bddng prces but also on ther bddng prces and status n the prevous aucton round. Reserv. Prce dw wpwl dl Revenue Farness for ~R dw for ~R dw : Increase : Decrease ~: Close to Table 1. The nterrelatonshp of customer s classes The reverse case (.e., decreasng the reservaton prce) ncreases farness by decreasng the number of unts avalable for the bdder drop control, and may ether 0

6 ncrease or decrease the total revenue of the e-servce provder. Accordngly, n decdng the upper bound of the reservaton prce, the e-servce provder should balance an ncrease n the total revenues versus the loss of farness nduced by the selected reservaton prce. As shown n Fgure 5, based on many experments conducted under the varous customer wealth dstrbutons, we dscerned 2/3 rule (.e., every two out of three tme-senstve resources should be allocated to the DW class) for nearly optmal dstrbuton of the tme-senstve resources between the DW class and the pool of resources reserved for the bdder drop control algorthm. Allocaton of 60% to 70 % of tme-senstve resources to the DW class n each aucton round can acheve the e-servce provder s desred revenue and mnmze the loss of farness. Ths rule leads to a smple and adaptve formula for the e- servce provder optmal bddng prce b 0. It should be set to the maxmum of the two values: the 2 R /3-th hghest bd n the current aucton round and C m, the mnmum cost of a unt of the traded resources. Fgure 5. The Optmal Dstrbuton of Resources 4. Dscusson of Expermental Results 4.1 Expermentaton Scenaros In our expermentaton, auctons are executed 2000 tmes recurrently and the followng scenaros are smulated Aucton Mechansm We compare the followng fve aucton mechansms wth multple wnners, one tme sealed bd and dscrmnatory prcng for sellng sngle tem homogeneous tme-senstve e-servce recurrently. (1) Tradtonal Aucton (TA) denotes an aucton mechansm that has no bdder drop control mechansm. In TA, bdders drop out of the recurrng aucton as a result of starvaton. (2) Tradtonal Aucton wth o Bdder Drop Assumpton (TABDA) represents a tradtonal aucton mechansm n whch bdders never drop durng the recurrng aucton n spte of starvaton (.e., despte the consecutve losses n the recurrng aucton). (3) Reservaton Prce Aucton (RPA) represents the TA wth reservaton prce. (4) Cancelable Aucton (CA) denotes aucton mechansm n whch the e-servce provder cancels an aucton round when the projected revenue does not meet her expectaton. (5) Optmal Recurrng Aucton (ORA) represents an aucton mechansm that supports the VLLF-BDC algorthm descrbed n the prevous secton. The expermental results of TABDA are mpossble to acheve n the real recurrng aucton, because the no bdder drop assumpton s unrealstc. In the real world, starvaton, trggered by the uneven wealth dstrbuton, wll cause bdders drop. Thus, n our expermentaton, TABDA s only used for comparson Wealth dstrbuton and mnmum cost of unt of tme-senstve resources The wealth of each customer lmts her wllngness to pay (.e., her unt of resources valuaton) n the aucton. For ths reason, we can nterpret the wealth dstrbuton as a dstrbuton of the upper bound on wllngness to pay. We set the e-servce provder s mnmum cost of a unt of the resources (e-servces) at 5. Thus, we set the reservaton prce of RPA as 5, too. We consder three types of the standard dstrbutons of the upper bound on wllngness to pay among the customers, all wth the mean of 5: (1) the exponental dstrbuton, (2) the unform dstrbuton over [0, 10] range, and (3) the Gaussan dstrbuton Bdders, Bddng Behavor and Goods There are 100 customers n our experments. Intally, all are actve,.e., all are bdders. We assume that the ntal bddng prce s randomly selected from the range [ t 2, t ], where t represents the upper bound on customer wllngness to pay. The sealed bddng assumpton makes each bdder s bddng behavor ndependent of others. However, n a recurrng aucton, the bddng behavor s nfluenced by the results of the prevous aucton rounds,.e., the wn/loss decson nformed to each bdder. Based on the assumpton of rsk neutral bdders, each bdder wll maxmze ts expected proft. All the above consderatons motvated us to assume the followng

7 bddng behavor. If a bdder lost n the last aucton round, she ncreases her bddng prce by a factor of α > 1 to mprove her wn probablty n the current round. The ncrease of bddng prce s lmted by the upper bound on bdder s wllngness to pay. If a bdder won n the last aucton round, she, wth equal probablty of 0.5, ether decreases the bddng prce by a factor β or mantans t unchanged. The decrease attempts to maxmze the expected proft. α and β are set n the experments to 1.2 and 0.8, respectvely. The mnmum bddng prce of a bdder s 0.1. If a bdder drops out of an aucton, hs bddng prce s set to 0. There are 50 unts of resources (.e. tme-senstve e-servce unts) avalable for allocaton n each aucton round Tolerance of Consecutve Losses The customer s tolerance of consecutve losses, abbrevated as TCL, denotes the maxmum number of consecutve losses that a customer can tolerate before droppng out of an aucton. TCL of each customer s unformly dstrbuted over the range of [2, 10]. 4.2 Analyss of Results Our experments focus on revenues of the e-servce provder and on farness of resource allocaton. An aucton s entrely far f a bdder wth a bd hgher than a wnner s a wnner as well. In our experments, the e-servce provder s revenue s proportonal to the average bddng prce of wnners n each aucton round, so we use the latter as a measure of the former. We also measure the number of wns for each customer n 2000 rounds of the recurrng aucton. The resultng dstrbuton s a metrc of farness, because hgher bddng customers should be more frequent wnners than the lower bddng ones. Farness of TABDA s optmal, because a bdder wth the bd hgher than a wnner s also a wnner. Addtonally, by the no bdder drop assumpton, TABDA never looses a customer wth hgh wllngness to pay and low TCL. Ths means that TABDA prevents the loss of farness that may result from low TCL. Thus, we can measure the loss of farness of TA, RPA, CA and ORA by ther degree of devaton from the farness of TABDA. We measure loss of farness LF k of the aucton mechansm k by the dstrbuton of wns between the customers: n = 1 WTABDA() Wk () LFk = 100, (8) R Total _ Aucton where n denotes the total number of customers n the recurrng aucton, WTABDA() and Wk () represent the total number of wns by bdder durng Total _ Aucton of aucton rounds n TABDA and aucton mechansm k, respectvely. In TA, an nevtable bdder drop problem s the domnatng factor that decreases the e-servce provder s revenue, because there are no wasted tmesenstve resources. As descrbed earler, the bdder drop problem results n a plunge of the average bddng prce of aucton wnners n the long run. In RPA, the revenue of e-servce provder s manly decreased by the resource waste problem. The effect of bdder drop problem on revenue s small n ths case, because the reservaton prce prevents the wnners from decreasng ther bddng prce to the very low level. However, RPA does not avod the resource waste problem. As a result, the e-servce provder cannot acheve her desred revenue n the recurrng aucton of ths type. CA suffers from the same problem as RPA. By cancelng aucton, CA can prevent remanng customers from decreasng ther bddng prce to the very low levels. However, the resources wasted n the cancelled aucton wll prevent the e-servce provder from achevng the desred revenue n CA. ORA s able to mantan prce competton permanently n a recurrng aucton thanks to the effcent bdder drop control. Moreover, n ORA, the resource waste problem never arses, because the entre stock of tme-senstve resources s sold n each aucton round. Therefore, the e-servce provder can preserve nearly optmal level of the revenue. As shown n Fgure 6, the bdder drop and resource waste problems arse under all smulated wealth dstrbutons n our expermental scenaros. The loss of farness of ORA s remarkably lower than the one observed n TA, RPA and CA under all smulated wealth dstrbutons of customers. Ths phenomenon results from the fact that TA, RPA and CA cannot prevent the loss of farness caused by hgh true value bdders droppng out of an aucton as a result of exceedng ther TCLs. In other words, TA, RPA and CA cannot prevent a customer who s wllng to pay hgh prces but has low TCL from droppng out of an aucton after exceedng hs TCL at some aucton round. In each aucton round, TA, RPA and CA have hghest possble farness, because ther wnners are selected by the current bddng prce only. Yet,

8 remarkably, ORA has lower loss of farness over the entre recurrng aucton because loss of farness that results from TCL s the domnatng factor n the long run. The specfc results measurng the loss of farness under varous customer wealth dstrbutons are provded n Table 2. Fgure 6. Average wnnng prce of wnners Exponental Unform Gaussan TA 34.6 % 23.9 % 29.4 % CA 33.5 % 32.9 % 33.4 % RPA 30.0 % 28.9 % 41.8 % ORA 9.4 % 6.0 % 11.9 % Table 2. Loss of Farness We also smulated the more general case of an aucton n whch a bdder who dropped out can return when the wnnng prce becomes suffcently low. For ths case, the expermental results show that the revenue of the e-servce provder settles somewhere between the revenues of TA and TABDA because those are the border cases of the general one. The revenue of the TA case sets the lower bound for the revenues n the general case because there are no bdders returnng durng the recurrng aucton. The revenue of TABDA sets the upper bound because all bdders return mmedately to the recurrng aucton n that case. In summary, ORA can acheve the ncreased revenue and the decreased loss of farness n the recurrng aucton for tme-senstve e-servces by resolvng the bdder drop problem and the resource waste problem. 5. Conclusons and Future Works Snce aucton mechansm s a competton based dynamc prcng mechansm, the bdder drop problem s one of the most mportant factors n desgnng auctoneer s strategy n the recurrng aucton. Resolvng ths problem for tme-senstve e-servces stablzes revenue of e-servce provder by preventng the collapse of prce compettons. Another problem that should be consdered for maxmzng e-servce provder s revenue s the resource waste. The tradtonal aucton mechansms, ncludng seller s optmal auctons, do not address these problems. The proposed ORA mechansm stablzes and ncreases the revenue of the e-servce provder by resolvng the two problems mentoned above. Ths mechansm also decreases the loss of farness by preventng the drop of bdders who have hgh wllngness to pay durng the recurrng aucton. In future works, we plan to study more effcent bdder drop control algorthms. We also plan to nvestgate a more general case of recurrng aucton n whch heterogeneous multple unt of tmesenstve e-servces are traded. Fnally, we wll also study the theoretcal underpnnngs of the proposed aucton mechansm. REFERECES [1] R. H. Frank and B.S. Bernanke, Prncple of Economcs: 2 nd edton, McGraw Hll, ew York, [2] A. Twana and B. Ramesh, e-servce: Problems, Opportuntes, and Dgtal Platforms, n proceedng of the 34 th Hawa Internatonal Conference on System Scence, [3] M. Bchler, The Future of e-markets: Multdmensonal Market Mechansm, Cambrdge Unversty Press, [4] J.G.Rley and W.F.Samuelson, Optmal Aucton, The Amercan Economc Revew, Vol. 71, o. 3, Jun [5] A. Fat and A.V. Goldgerg, J.D. Hartlne, and A.R. Karln, Compettve Generalzed Aucton, n Proceedng of 34 th Annual ACM symposum on Theory of computng, [6] R. McAfee and P.J. McMllan, Aucton and Bddng, Journal of Economc Lterature, Vol. 25, 1997, pp [7]W. Vckrey, Counter speculaton, Aucton, and Compettve Sealed Tenders, Journal of Fnance, Vol. 16, o. 1, March [8]L. Ausubel and P. Cramton, Vckrey Auctons wth Reserve Prcng, Economc Theory, 23, Aprl 2004, pp [9] J.S. Lee and B.K. Szymansk, An Analyss and Smulaton of a ovel Aucton-Based Prcng Mechansm for etwork Servces, Techncal Report TR-05-02, Department of Computer Scence, Rensselaer Polytechnc Insttute, Jan [10] J.S. Lee and B.K. Szymansk, Stablzng Market va a ovel Aucton based Prcng Mechansm for Short-Term Contracts for etwork Servces, 9 th IFIP/IEEE Internatonal Symposum on Integrated etwork Management (IM2005), ce, France, [11] V. Krshna, Aucton Theory, Academc Press, 2002.

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