Pricing Differentiated Internet Services


 Sibyl Price
 3 years ago
 Views:
Transcription
1 1 Pricing Differentiated Internet Services Linhai He and Jean Walrand Dept. of EECS, U.C. Berkeley Abstract One of the critical challenges facing the networking industry today is to increase the profitability of Internet services. One wellknown method in economics for increasing the revenues of a service is to segment its market through differentiation. However, special characteristics of Internet services, such as congestion externality, may complicate the design and provisioning of such offerings. In this paper, we study how a provider should price its services differentially based on their characteristics. By using a gametheoretic approach, we show that even with a simple twoclass differentiated service model, if prices are not properly matched with service qualities, then the system may settle into an undesirable equilibrium similar to that in the classical Prisoner s Dilemma game. In addition, there may not even be a stable equilibrium under certain conditions. We then show that dynamic pricing approaches, in which prices are chosen according to users relative preferences over different service classes, may be used to avoid such types of problems. Index Terms Pricing, differentiated services, market segmentation, game theory. I. INTRODUCTION For historical reasons, most of the Internet service providers (ISP) today offer only one type of service, namely, the besteffort service to the Internet users. All networking applications at present are designed based on this service model, which does not provide any guarantee on its quality. On the other hand, as new applications, such as Voice over IP and streaming video, are becoming popular, users may benefit from Internet services with higher quality and hence may be willing to pay extra money for them. Therefore, if they become available, differentiated Internet services (DIS) would benefit both the ISPs and the Internet users. Internet service providers do seem to be moving in that direction. Recently, some ISPs have started marketing basic versions of DIS. One example is NetZero, which is a nationwide ISP offering consumers a choice of three This research is supported by DARPA under Grant No. BAA0018 and by NSF under Grant ANI dialup Internet access options to meet their budget and personal Internet access needs [3]. Those access options are priced differently according to the download speeds they provide. Past work has studied how an provider should provision its resources to implement different classes of services. In this paper, we focus on the other dimension of the problem the pricing issue, i.e. how should an ISP price its service classes differently based on their respective quality? It may seem trivial at first, as an ISP s primary objective is to maximize its revenue, which is the product of price and demand. However, as we will demonstrate in this paper, because of unique characteristics of Internet service [2], such as congestion externality and individual users strategic choices, demand for different service classes may change with their prices in complicated ways. Consequently, pricing schemes need to be carefully designed to avoid undesirable outcomes for the ISPs. In the rest of the paper, we will first describe a DIS model and our assumptions on users behaviors in Section II. We then introduce two simple examples to demonstrate possible instability and inefficiency issues in providing DIS, when they are improperly provisioned. In Section IV, we propose two dynamic pricing schemes to address those issues. In Section V, we discuss ISPs economic incentives in providing DIS. Finally, we conclude the paper with a summary and discussions on future research. II. MODELS Consider an ISP offering two classes of service to its users. These two classes share a common set of resources, such as link capacity and buffer spaces, through some workconserving scheduling policy. Those two classes are priced at p 1 and p 2, respectively (without loss of generality, assume p 1 > p 2 always). Each user chooses independently which service class to use, based on factors such as the prices and the levels of service quality that they experience. Note that in our model the service provider does not provision any explicit level of service quality for the two classes. Instead, they are determined by the aggregation of users individual
2 2 choices. When the prices are fixed, a user chooses the class with the performance that best suits her need. But when too many users choose the same class and cause the service quality to degrade, some users in that class may decide to leave, for the decreased net benefit this class provides. Consequently, the deflection of these users then helps stabilize the degradation in service quality. The main motivation behind this selfregulated service model is its flexibility. Today, there are many types of applications running over the Internet, each of which may have different requirements in service quality. But with this service model, an ISP does not need to know much about users preferences to provision its services. In fact, their actual performance is adaptively determined by users own choices, i.e. the market demand. More specifically, if users can reach an equilibrium in their choices, i.e. a state from which no one would unilaterally deviate, then the class with higher price must have better service quality, because otherwise users in that class would not pay more for it. Therefore, this service model allows ISPs to adapt quickly to any change in users preference and willingness to pay, and the types of users they serve, without actively monitoring and learning about them. This minimalist approach shares the same philosophy with the socalled ParisMetro model for Internet services [4]. In that model, service providers deploy two identical but physically separate networks and charge them differently to achieve service quality differentiation. We believe that for an Internet service, the performance measure that matters most to the end users is delay. This is because at the application level, what ultimately determines a user s perception about the quality of a service is how soon information can be sent and received, e.g. how long it takes to fetch a web page, or how much a voiceoverip packet is delayed when sent across the Internet. Therefore, for the purpose of analysis, we assume a user s decision is made based on the maximization of her net benefit, defined by the following quasilinear objective function: max J u = ω u f u (T i ) p i. (1) i=1,2 Here T i is the delay experienced by user u if she chooses to use service class i. The function f u is a bounded, differentiable, decreasing function of T i. In addition, for the convenience of analysis, we assume f u (t) 0 as t, but f u (t) 0 for any t R +. The scaling parameter, ω u R +, is unique to each user and indicates each user s sensitivity to the price p i. In other words, ω u models a user s willingness to pay (WTP). So the product, ω u f u (T i ), indicates user u s utility from using B A Class 1 Class 2 Class 1 f a (T 0 ) p 1 f b (T 0 ) p 1 f a (T 2 ) p 2 f b (T 1 ) p 1 Class 2 f a (T 1 ) p 1 f b (T 2 ) p 2 f a (T 0 ) p 2 f b (T 0 ) p 2 Fig. 1. User a and b s net benefits corresponding to different combinations of their choices. service class i when its delay is T i. In this paper, we assume each user generates a fixed amount of traffic (i.e. no flow control is applied), so that with appropriate scaling, the cost of using service class i for a user equals the price of that class. In addition, users do not randomize in which class they use, nor split their traffic between two service classes. Lastly, we assume the service provider is also a strategic player. Its main objective is to maximize its own interest. III. MOTIVATING EXAMPLES In this section, we illustrate some of the issues may arise in pricing DIS, through two simple cases. In these two cases, there are two users (u = 1, 2) with the same WTP parameters, ω u = 1. The traffic they generate is exchangeable and does not depend on which service class they choose. When both users choose the same class, the resulting delay for them is the same and is denoted by T 0. When they choose differently, the user in the higherprice service class experiences a smaller delay (denoted by T 1 ) than the other does (denoted by T 2 ). Since the scheduling policy is work conserving, we have T 1 < T 0 < T 2 and T 1 + T 2 = 2T 0. We can see that one user s choice affects the amount of delay that the other may experience. This interdependency between each other s choice leads to a strategic game [5] played between the users. The table in Figure 1 lists both users net benefits corresponding to different combinations of their choices. In each entry of the table, the first row corresponds to user 1 s net benefit, and the second row is for user 2. We are interested in finding what equilibrium [5] this game may have. We first show that no purestrategy Nash equilibrium would exit if two users have different preferences in whether to share the same service class or not. Without loss of generality, assume user 1 does not prefer to share the same service class with user 2, whereas user 2 prefers the opposite. This happens only if f 1 (T 0 ) f 1 (T 2 ) < p 1 p 2 < f 1 (T 1 ) f 1 (T 0 ), f 2 (T 1 ) f 2 (T 0 ) < p 1 p 2 < f 2 (T 0 ) f 2 (T 2 ).
3 3 Or equivalently, f i s should have the following properties: f 1 (T 1 ) + f 1 (T 2 ) > 2f 1 (T 0 ), and f 2 (T 1 ) + f 2 (T 2 ) < 2f 2 (T 0 ). Since T 1 + T 2 = 2T 0, a sufficient condition for the above to hold is that one of them is convex and the other is concave. As an example, user 1 may be running data applications whose throughput decreases quickly as delay increases. Whereas user 2 may be running realtime applications so that her utility decreases slowly with small amount of delay but diminishes quickly after the delay exceeds certain threshold. The nonexistence of an equilibrium implies that neither user would be able to settle in her choice of classes. Both users would keep switching between classes for better net benefit for themselves. It is very likely that eventually both users are unhappy about the uncertainty in the service quality they experience and decide to leave, causing a loss of revenue for the provider. We next show that even if a purestrategy Nash equilibrium exists, it may not be desirable for both users. Consider a case in which the prices satisfy the following condition f i (T 0 ) f i (T 2 ) > p 1 p 2, for i = 1, 2. (2) It is straightforward to verify that this game has a unique Nash equilibrium. At this equilibrium, two users share the same service class, but they both choose the more expensive class 1 instead of class 2! Clearly, both of them could have been better off if they chose to use class 2. In that case, they could have the same delay T 0 but pay a lower price p 2, thus achieving higher net benefits for both of them. This outcome closely resembles that of the classical Prisoners Dilemma game [6], in which both players end up in an undesirable equilibrium because of their selfish moves. We believe this dilemma happens because the degree of differentiation in the service qualities mismatch with that in the prices. When class 1 offers better quality than class 2 does, but p 1 is not much higher than p 2, both users have a strong incentive to use class 1, consequently causing degradation in the service quality of that class. As the above two simple examples have shown, it is important for the service provider to match its prices appropriately with the service qualities. In the next section, we extend the above results to manyuser cases and investigate how to design pricing schemes to achieve stable and efficient equilibrium. A. ManyUser Model IV. PRICING SCHEMES In this model, we assume that there are infinite number of atomic users, each of which generates infinitesimal amount of traffic. Their objective functions are the same as the one described in (1), except that all users have the same f( ) function, but different WTP parameter ω. We assume there is a density function, ρ(ω), associated with ω, so that a group of users with a continuum of WTP parameter over the range (ω 1, ω 2 ) generate a total traffic load of ω 2 ω 1 ρ(ω)dω. The shape of the function ρ(ω) hence indicates the distribution of WTP among the users. Without losing too much generality, we assume that ρ(ω) is nonnegative, differentiable and has support over R +. In addition, we assume ωρ(ω) dω is finite, i.e. a mean value of ω exists. With this model, we say a Nash equilibrium is reached if no single user has an incentive to unilaterally change her choice [5]. Proposition 4.1: Nash equilibrium exists for the game described above. Proof: If an equilibrium exists, define the load at each class by x i, and their corresponding delays by T i. Note that T i is a function of both x 1 and x 2. By the definition of Nash equilibrium, this equilibrium should have the following properties: 1) If any user choose to use class 1, then her WTP parameter must satisfy the following condition, ωf(t 1 ) p 1 > ωf(t 2 ) p 2, for class 1 must provide higher net benefit for her. Since p 1 > p 2, and f( ) is a decreasing function, we then have T 1 < T 2. This confirms our assertion earlier that if equilibrium exists, the class with higher price would offer better service quality. 2) For any user a and b with ω a < ω b, if user a chooses to use class 1, user b would choose to use class 1 as well. This is because if user a chooses to use class 1 at equilibrium, the following conditions must be satisfied: ω a f(t 1 ) p 1 > ω a f(t 2 ) p 2, or ω a (f(t 1 ) f(t 2 )) > p 1 p 2, So by ω a < ω b, ω b (f(t 1 ) f(t 2 )) > p 1 p 2, or ω b f(t 1 ) p 1 > ω b f(t 2 ) p 2. User b prefers to use class 1 as well, because it offers higher net benefit than class 2 does.
4 4 3) By continuity assumption on ρ(ω), the above argument then implies that there must exist a marginal user with WTP parameter ω 1 that satisfies the following condition: ω 1 f(t 1 ) p 1 = ω 1 f(t 2 ) p 2, (3) so that all users with WTP parameter ω > ω 1 choose to use class 1 at the equilibrium. 4) By similar arguments, for any pair of users a and b with ω a > ω b, if user a decides not to join the system at all because she cannot find a class that offers nonnegative net benefit, then user b would make the same choice. Moreover, there must exist a marginal user with WTP parameter ω 2 that satisfies the same following condition: ω 2 f(t 2 ) = p 2, (4) so that all users with WTP parameter ω < ω 2 choose not to join the system. 5) Finally, for all users with WTP parameter ω (ω 2, ω 1 ), they choose to use class 2, because by the definition of ω 1 and ω 2, ωf(t 1 ) p 1 < ωf(t 2 ) p 2, and ωf(t 2 ) > p 2. Based on the above properties, the existence of Nash equilibrium then depends on if there exists a solution {ω 1, ω 2 } to the following system of fixedpoint equations: { ω1 (f(t 1 ) f(t 2 )) = p 1 p 2, ω 2 f(t 2 ) = p 2. Since f is bounded and differentiable, the mapping between {ω 1, ω 2 } defined by the above mapping is continuous and compact. Therefore, by Brower s fixedpoint theorem, there exists at least one solution to the above equations. However, for any generic f and T i functions, this proposition does not provide additional information about the Nash equilibrium other than its existence. Next we show that for certain combinations of those functions, there may be multiple equilibria and some of those may not be stable or efficient. As we will see, they closely resemble those equilibrium presented in Section III. First, let us consider a small perturbation applied to the Nash equilibrium. Without loss of generality, suppose some users with ωs in a small neighborhood ɛ of ω 1 have switched from class 2 (their choices at equilibrium) to class 1. The change in their net benefits after the move is the following: = ɛ ω 1 ρ(ω 1 ) { f (T 1 ) ( T1 T 1 ) ( )} (5) f (T 2 ) T2 T2 If > 0, then the net benefits of this group of users actually increase after they switch the classes. Consequently, these users have incentive to stay in class 1, rather than going back to class 2. For the same reason, it can be shown that there are also a group of users who choose to use class 1 at Nash equilibrium but have incentive to switch to class 2 when the equilibrium is perturbed. This deviation from the equilibrium under perturbation suggests that this Nash equilibrium is not stable. In real operations, users experiment with the system in a randomized way. Therefore, one may expect that the exact Nash equilibrium could never be reached if it is not stable. What would happen instead is that a group of users whose ωs fall within some neighborhood around ω 1 would switch back and forth between two classes. In the long run, such an outcome clearly is not very desirable for both users and the ISP. This instability condition (i.e. > 0) in fact is not difficult to meet. One example is the following. Suppose f is a concave function of T i. Then because T 1 < T 2, f (T 1 ) > f (T 2 ). A sufficient condition for > 0 is to have T 2 > T2 T 1 + T2 (6) > T1 + T2 What these conditions suggest is that if under a scheduling policy, a user exerts more congestion effect on users in the other class than those in her own class, then the resulting Nash equilibrium may not be stable. It is easy to verify that for a wide range of values of x i s, strictpriority scheduling is one of such scheduling policies. In addition to stability, scheduling policy together with the function f also have effect in the multiplicity of the Nash equilibrium. A necessary condition is that d(ω 1 ) ω 1 (f(t 1 ) f(t 2 )) is not a monotonic function of ω 1, with w 2 as an implicit function of ω 1 defined through condition (4). Figure IV A shows one of such examples. Here the classes are served by strictpriority policy, the utility function is f(t ) = (T/10) 2, and ρ(ω) is uniform over [0, 20] with a total load of The prices for the two classes are p 1 = 4, and p 2 = 1. Their difference (i.e. p 1 p 2 ) is shown in the plot by the horizontal line. So
5 U(ω 0 ) p 1 p 2 Nash Equilibrium Nash Equilibrium (unstable) p 1 = 4, p 2 =1 x(ω) ~ unif(0,20) f(t) = 2.5*[1 (T/10) 2 ] ω c ω 0 Fig. 2. Multiple equilibriums of a game when strictpriority scheduling is used. its two intersections with d(ω 1 ) correspond to the two Nash equilibria of the game. The slope of d(ω 1 ) at these two intersections indicates the stability of those two equilibria. For instance, the downward slope at the right one indicates that when ω 1 is perturbed slightly to the left, i.e. some users move into class 1 from class 2, then d(ω 1 ) will increase, which corresponds to a positive. Hence this equilibrium is unstable. To the contrast, the upward slope at the left one indicates that when ω 1 is perturbed slightly to the left, i.e. some users move into class 1 from class 2, then d(ω 1 ) will decrease, which corresponds to a negative. Hence this equilibrium is stable. Although the equilibrium at the left is stable, we can see that a majority of the users choose to use more expensive class 1. This results in a longer average delay for all users, when compared to the one given by the other equilibrium, if it can be reached. Therefore, this outcome can be viewed as a generalization of that in the Prisoner s Dilemma game described in Section III. This kind of outcomes clearly should be avoided. In the rest of this section, we investigate how to design pricing or scheduling schemes to ensure stable and efficient equilibrium. B. Stable Pricing Schemes We first investigate how to design the system so that it can lead to a stable equilibrium. First, one may conjecture from the previous analysis that the stability of the Nash equilibrium is directly related to the degree of coupling between two service classes. In this regard, strictpriority scheduling and the ParisMetro model obviously represent two opposite extremes among all scheduling policies. Under strictpriority scheduling, the highpriority class has the most impact on the other class, whereas ParisMetro model provides the most isolation because two service classes are physically separated. In fact, under the ParisMetro model, [4], both cross partial derivatives are zero. defined in (5) thus becomes ( = ω 1 ρ(ω 1 ) f (T 1 ) T 1 + f (T 2 ) T ) 2 < 0. Therefore, ParisMetro model always has a stable equilibrium. However, it is questionable if any ISP would adopt the ParisMetro model to provide differentiated services. First, it is inflexible, because the resources allocated to the two classes are fixed and cannot be optimized when ρ(ω), i.e. the mix of different types of users, changes. Second, because resources allocated to the two classes cannot be shared, one may expect there may be some loss in efficiency, hence loss in revenue, for the ISP. Other workconserving scheduling policies, such as weightedfair queueing, may not lead to unstable equilibrium as easily as the strictpriority policy does, as long as they do not have strong crossclass congestion effect. However, they still need to be carefully provisioned to match well with the prices. For instance, for a weighted fair queueing based system with a small difference in the prices, if the weights assigned to the two classes are far apart, then the system would behave similarly to the one with strictpriority policy and has a high risk in getting into the instability problem. On the other hand, if the weights are set too close for the sake of avoiding instability, then there is little differentiation in service quality. Therefore, how to choose the right amount of differentiation in price determines all other issues in service provisioning. In the following, we investigate how to design pricing schemes to achieve stable equilibrium for any type of scheduling policy. As we have argued earlier, unstable equilibrium is caused by a strong crossclass congestion effect. Since scheduling policy is fixed, we may use the prices to regulate the traffic load distributed between classes, as a means to prevent the system from moving into the unstable region. Based on this idea, we keep p 2 constant as before, but make price p 1 a function of x 1. More specifically, we set p 1 = p 2 + g(x 1 ), where g(x 1 ) is an increasing, differentiable function of x 1 over [0, 1], and g(0) = 0. Next, we show that Nash equilibrium still exists with this new pricing scheme, then derive conditions on g(x 1 ) that would ensure stable Nash equilibrium. Proposition 4.2: The game with the above modified pricing function has a Nash equilibrium. Proof: Omitted. All the arguments in Proposition 1 still apply, with necessary modifications to accommodate g(x 1 ). Now consider a user who chooses to use class 2 at
6 6 equilibrium. Her ω must satisfy the following condition δ = ω(f(t 1 ) f(t 2 )) g(x 1 ) < 0. To ensure stability, the net benefit of a user should always decrease when she switches away from the equilibrium. Therefore, a sufficient condition for that is δ < 0, or dg dx 1 > ωρ(ω)[f (T 1 )( T 1 T 1 ) f (T 2 )( T 2 T 2 )] It can be verified that the same condition applies for users in class 1 switching to class 2. Here we have assumed that users who choose to stay in the system is not affected by a single user s move, because the amount of traffic she generates is infinitesimal. Since both ωρ(ω) and f (T i ) are bounded, a sufficient condition for the above inequality to hold is dg dx 1 > K ( T1 + T 2 T 1 T 2 ), where K is a bound on ωρ(ω) f (T ). To eliminate x 2 from the above condition, we may take sup of its righthand side over [0, ρ a ], which is the feasible range of x 2, then obtain the final sufficient condition for g(x 1 ): dg > K dx 1 sup x 2 [0,ρ] ( T1 + T 2 T 1 T 2 ). Please note that the terms in the parenthesis are the difference between the marginal congestion costs across service classes and that within classes. So if a scheduling policy has small marginal congestion cost across its service classes, e.g. the ParisMetro model, then the above difference is negative and hence fixed prices are sufficient to ensure stable equilibrium. Otherwise, p 1, the price for premium quality class, should be adjusted according to the load level in class 1, at a rate at least K times faster than that of the difference in the congestion costs. C. Efficient Pricing Scheme Next we show how pricing scheme may be designed to avoid Prisoner s Dilemma type of outcomes demonstrated in Section III. In this scheme, an ISP operates in a slightly different way as before. Instead of having fixed prices and unprescribed levels of service quality, on a short time scale, the ISP sets bounds for the maximum delay (denoted by D i, i = 1, 2.) permitted in each service class. Without loss of generality, we assume D 1 < D 2. For a given scheduling policy, these delay bounds may be translated into the maximum traffic loads permitted for each service class, which are denoted by λ i 1. The prices are adjusted to regulate the demand for each class, so that the delays do not exceed D i s. More specifically, p 2 (x 1, x 2 ) = p e 2 I{x 2 λ 2 }, p 1 (x 1, x 2 ) = p 2 (x 1, x 2 )I {x 1 < λ 1 } + p e 1 I{x 1 λ 1 }, (7) where I{ } is the indicator function, and p e i s are a pair of prices through which the ISP is able to regulate x i at the target level, λ i. After an equilibrium is reached under these prices, on a longer time scale, the ISP may experiment with different values of T i s to achieve its objectives, such as revenue maximization. The users still choose the service class that maximizes their net benefits. Since the prices now in turn depend on the aggregation of users choices, we need to know if Nash equilibrium exists for this scheme. If it does, then what the prices p e i are at the equilibrium. Proposition 4.3: Nash equilibrium exists in the game with the pricing function described in (7). Proof: If there exists a purestrategy Nash equilibrium, the delays in each service class should be D i, i = 1, 2; otherwise, the prices p e i s would not be at equilibrium. Then for any two users a and b with WTP parameter ω a and ω b, if user a chooses to use class 1 at equilibrium, so must be user b, because ω b (f(d 1 ) f(d 2 )) > ω a (f(d 1 ) f(d 2 )) > p e 1 p e 2. (8) Therefore, all users in class 1 at equilibrium must be those with WTP parameters in the range of [ω 1, ), where ω 1 satisfies the following condition, ω 1 ρ(ω) dω = λ 1. (9) In addition, the prices should satisfy the condition that for any ω < ω 1, ωf(d 1 ) p e 1 < ωf(d 2 ) p e 2, (10) i.e. those users who are less willing to pay than ω 1 would not have incentive to stay in class 1. Combining (8) and (10), we can conclude that p e 1 p e 2 = ω 1 (f(d 1 ) f(d 2 )). (11) This condition sets the difference between the prices of two service classes. By a similar argument, if user a with ω a chooses to stay in class 2 at equilibrium, then user b with ω b > ω a would choose to stay in class 2 as well, provided that ω b < ω 1. Therefore, at equilibrium, all users in class 2 1 We assume λ 1 + λ 2 < ρ a, so that users with small ωs are left out of the system
7 7 are those with ω [ω 2, ω 1 ], where ω 2 is determined by the following constraint: ω1 ω 2 ρ(ω) dω = λ 2. (12) Accordingly, price p e 2 needs to be set sufficiently high, so that ω < ω 2, ωf(d 2 ) < p e 2, i.e. those users who are less willing to pay than ω 2 would not have incentive to join class 2. In addition, by the fact that ω < ω 2, ωf(d 1 ) p e 1 < ω 2 f(d 1 ) p e 1 = ω 2 f(d 1 ) p e 2 ω 1(f(D 1 ) f(d 2 )) = (ω 2 ω 1 )f(d 1 ) + (ω 1 ω 2 )f(d 2 ) = (ω 1 ω 2 )(f(d 2 ) f(d 1 )) < 0, where the first equality is due to (11), those users would not choose to use class 1 either, for it offers negative net benefit to them. Combining the above arguments, we can completely specify the prices p e i at equilibrium by the following: p e 2 = ω 2 f(d 2 ), p e 1 = ω 1 (f(d 1 ) f(d 2 )) + p e 2 = ω 1 f(d 1 ) (ω 1 ω 2 )f(d 2 ). (13) We now argue that the Nash equilibrium exists and in fact is unique. For any pair of λ i, according to (9) and (12), there are a unique pair of ω i, which uniquely determine a pair of p e i, according to (13). These ω is and p e i s together completely specify the equilibrium. Next we show that this Nash equilibrium in fact is socially efficient, i.e. it maximizes the sum of all users utilities, by comparing it with to the outcome of a Vickrey auction [7] designed according to the VCG mechanism [8]. In this Vickrey auction, users are asked to submit their WTP parameters to the ISP. Based on the collected information, the ISP then assigns the users to the service classes in a socially efficient way. The users are charged according to which class they are assigned to. These charges are carefully designed, so that it is in a user s best interest to submit the true value of her WTP parameter. Similar schemes have been proposed for congestion pricing in the Internet [9] [10]. Proposition 4.4: The equilibrium specified in (9), (12), and (13) is the same as the outcome generated by the Vickrey auction described above. Proof: Since users have the same preference function f, the optimal assignment rule for maximizing the social welfare is to sort the users by their WTP parameters in descending order and then assign them first to class 1 until the maximum load λ 1 is reached, and then to class 2, until λ 2 is reached. This assignment is socially efficient because a swapping between the assigned classes of any two users would not affect others, due to the assumption that all users traffic is exchangeable, yet would decrease the sum of these two users utilities. According to the VCG mechanism, to incentivize a user into revealing the true value of her WTP parameter, the price charged her should equal her externality to others, i.e. the difference in the total social welfare between the case in which she participates in the mechanism and the case in which she does not. Therefore, in our model, all users in class 2 should be charged with a price of ω 2 f(d 2 ). This is because if any of them is removed from the system, the user who presently is not assigned to either classes but now can move into class 2 is the one whose WTP parameter is right before ω 2. With other users unaffected, the change in the total social welfare equals her improved utility, which is ω 2 f(d 2 ). For any user u in class 1, her absence can affect two users. One is the user whose WTP parameter is right after ω 1. She is assigned to class 2 if user u is present, but can be moved up to class 1 when user u is removed from the system. This move can increase her utility by ω 1 (f(d 1 ) f(d 2 )). Moreover, her move to class 1 creates an open space in class 2, so that the user whose ω is right after ω 2 now can join class 2, instead of being kept out of the system. This user s utility consequently increases by ω 2 f(d 2 ). Therefore, the change in the total social welfare is the sum of the utilities of these two affected users, which is ω 1 (f(d 1 ) f(d 2 )) + ω 2 f(d 2 ). This gives the price ought to be charged to user u. Comparing with the equilibrium generated by our dynamic pricing scheme, we can see that the socially efficient Vickrey auction uses the same assignment rule and charges the same prices for the service classes. Yet our pricing scheme is simpler and more practical to implement, because it requires little communication between the ISP and the users. V. INCENTIVES FOR MARKET SEGMENTATION In this section, we investigate an ISP s incentive in providing differentiated services in two cases. In the first case, users have homogeneous utility function; but in the second one, there is nonzero variance in users WTP paramters. A. Homogeneous Users Proposition 5.1: If all users have the exact same utility functions, then an ISP can generate no more revenue
8 8 than it could with a single service class. Proof: Consider a group of users generating a total load of ρ a. For convenience, assume their WTP parameters are all equal to one. For the time being, assume that the provider is required to keep all users in the system. This constraint will be relaxed later in the proof. If the provider offers only one class of service, then the highest price it can charge under the aforementioned load constraint is p 0 = f(t 0 ), where T 0 is the delay of the corresponding FIFO queue under a load of ρ a. In this case, the provider collects a revenue of ρ a f(t 0 ). Now suppose that the provider offers two classes of services, priced at p 1 and p 2, respectively. Denote the load in class 1 by α, and the delay of class i by T i (α, ρ α), i = 1, 2. With a slight abuse of notation, define f i (α, ρ a α) f(t i (α, ρ a α)). Depend on the prices and the delay function T i s, there are three possible equilibria: 1) If f 1 (α, ρ a α) p 1 > f 2 (α, ρ a α) p 2, α [0, ρ a ], then the only Nash equilibrium for the game is α = ρ a, i.e. all users choose to use class 1. To keep all users in the system, p 1 needs to satisfy p 1 f 1 (ρ a, 0) = f(t 0 ), i.e. all users should have nonnegative net benefit. Therefore, the maximum possible revenue in this case is R = ρ a f(t 0 ). 2) If f 1 (α, ρ a α) p 1 < f 2 (α, ρ a α) p 2, α [0, ρ a ], then the only Nash equilibrium for the game is α = 0, i.e. all users choose to use class 2. To keep all users in the system, p 2 needs to satisfy p 2 f 2 (0, ρ a ) = f(t 0 ). Therefore, the maximum possible revenue in this case is R = ρ a f(t 0 ). 3) If α 0 (0, ρ a ) such that f 1 (α 0, ρ a α 0 ) p 1 = f 2 (α 0, ρ a α 0 ) p 2, then this is a Nash equilibrium for the game, because this distribution of the users makes the two service classes indifferent in term of the net benefit they provide. The revenue at this equilibrium thus is R = α 0 p 1 +(ρ a α 0 )p 2 = ρ a p 1 (ρ a α 0 )(p 1 p 2 ). Since α 0 increases as p 1 p 2 decreases, revenue R is a decreasing function of p 1 p 2. This implies that to increase the revenue, the provider should decrease the difference between p 1 and p 2 until α 0 reaches ρ a. At that point, p 1 is set to f 1 (ρ a, 0) = f(t 0 ) in order to keep all users in the system. Consequently, the maximum possible revenue in this case is R = ρ a p 1 = ρ af 1 (ρ a, 0) = ρ a f(t 0 ). The above arguments show that for any given carried load, the provider gains nothing more from offering multiple classes of service. Using this result, we then show that at their respective optimal loads, the same conclusion still holds. Suppose that the multiservice and the singleservice systems carry different loads, ρ fifo and ρ multi, at their respective optimum, R fifo and Rmulti. First, suppose that R fifo < R multi. Then by the arguments earlier, a singleservice system carrying the same amount of load as ρ multi would yield the same revenue as Rmulti. So ρ fifo cannot be the optimal load for the singleservice system, and its corresponding revenue cannot be the maximum revenue possible. This implies a contradiction. The same argument can be used to show that Rfifo cannot be larger than R multi either. Hence we conclude that Rfifo must equal R multi. B. Heterogeneous Users In this model, we assume that ρ(ω) has a nonzero variance and all the properties described earlier. Proposition 5.2: By offering multiple service classes, an ISP is able to collect more revenues than, or at least the same amount as, that with a single service class. Proof: As in the proof for the previous case, first consider the constraint that a total load of ρ a is to be carried by both multiservice and singleservice systems. The total revenue generated by a multiservice system is R multi = x 1 p 1 + x 2 p 2. As proved in Section IV, at equilibrium, p 2 = ω 2 f(t 2 ), and hence As a result, p 1 = ω 1 (f(t 1 ) f(t 2 )) + ω 2 f(t 2 ). R multi = x 1 ω 1 (f(t 1 ) f(t 2 )) + (x 1 + x 2 )ω 2 f(t 2 ) = x 1 ω 1 (f(t 1 ) f(t 2 )) + ρ a ω 2 f(t 2 ). Comparing it with the revenue generated in a singleservice system, R fifo = ρ a ω 2 f(t 0 ), we can see that R multi > R fifo only if x 1 ω 1 (f(t 1 ) f(t 2 )) > ρ a ω 2 (f(t 0 ) f(t 2 )). (14) Note that f(t 1 ) f(t 2 ) > f(t 0 ) f(t 2 ) always, as long as p 1 > p 2. Moreover, ρ a ω 2 is a constant with respect to p 1, because of the constraint to keep all of the given load ρ a. There are two possible cases to consider: Case 1. The condition is easily satisfied if x 1 ω 1 is an increasing function of ω 1, because then there must be a large enough ω 1 to satisfy the inequality 2. Since x 1 = ω 1 ρ(ω) dω, x 1 ω 1 is increasing only if the tail of 2 Note that we can use p 1 to lead the equilibrium to reach this ω 1
9 9 ρ(ω) decays slowly enough. In other words, there is a significant percentage of highpaying users. Case 2. If x 1 ω 1 is nonincreasing, it is uncertain whether there always exists a ω 1 to satisfy (14). However, the worst the provider can do is to choose its price so that ω 2 = ω 1, i.e. to have all users choose to use class 1. This is essentially equivalent to offering a single class of service, which let the provider collect the same amount of revenue as R fifo 3. Requiring a multiservice system to carry the same total load as a singleservice system obviously is suboptimal. But even in this case, the above results have shown that a provider should be able to generate at least the same amount of revenue by going from single service class to multiple service classes. So at the actual optimum, we can expect that the provider can do better with multiple service classes, especially when there is enough demand from the highpaying users. VI. SUMMARY AND FUTURE RESEARCH In this paper, we have studied issues in pricing differentiated Internet services. We have shown that when prices for different service classes are improperly chosen to reflect the differentiation in service qualities, the resulting system may have inefficient and even unstable operating equilibria. These undesirable outcomes may affect users degree of satisfaction about the offered services and cause possible loss of revenue for the service provider. To avoid these problems, we have proposed two dynamic pricing schemes. In one scheme, we have derived a sufficient condition on the pricing function to ensure a stable operating equilibrium; in the other, we have demonstrated how prices can be used to regular traffic loads in a way to achieve socially efficient equilibrium. We also have studied the incentives of the ISPs in offering differentiated services, in the presence of homogeneous and heterogeneous users. We have shown that by offering multiple service classes, providers are able to collect more revenues than that with a single service class in most practical cases. There are more related research issues worth investigating. First, we would like to extend our results to more general models. For example, the user model could be expanded to include multiple types of utility functions, representing the case where users running different types of applications have different preference over delay. Second, we are also interested in exploring pricing issues with multiple service providers, such as competition and peering. Gibbens, Mason and Steinberg [11] have shown in their paper that when two providers are in competition, they do not have economic incentives to offer multiple classes of services. However, this result is obtained based on the ParisMetro service model and is verified by numerical studies only. It would be interesting to investigate if their findings still hold for more general models and scheduling policies. REFERENCES [1] J. J. Gabszewicz, A. Shaked, J. Sutton and J. F. Thisse. Segmenting the Market: the Monopolist s Optimal Product Mix, Journal of Economic Theory, 39(2),27389, [2] P. Chander and L. Leruth. The Optimal Product Mix for a Monopolist in the Presence of Congestion Effects: A Model and Some Results, International Journal of Industrial Organization, 7(4), , [3] Netzero, [4] A. M. Odlyzko. Paris Metro Pricing for the Internet, Conf. on Electronic Commerce, [5] J. F. Nash. Equilibrium Points in NPerson Games, Proceedings of National Academy of Science, [6] D. Fudenberg and J. Tirole. Game Theory, MIT press, Cambridge, MA, [7] W. Vickery. Counterspeculation, Auctions, and Competitive Sealed Tenders, Journal of Finance, 16(1):837, Mar.1961 [8] A. MasColell, M. D. Whinston and Jerry R. Green. Microeconomic Theory, Oxford University Press,New York, [9] J. MackieMason and H. Varian. Pricing the Internet, Public Access to the Internet, B. Kahin and J. Keller, editors, Prentice Hall, Englewood Cliffs, NJ, [10] J. Shu and P. Varaiya. Pricing Network Services, Infocom, [11] R. Gibbens, R. Mason and R. Steinberg. Internet Service Classes under Competition, IEEE Journal on Selected Areas in Communications, 18(12), December 2000, pp It is straightforward to verify that p 1 = ω 2 f(t 0 ) in this case.
Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole
Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole Luís M. B. Cabral New York University and CEPR November 2005 1 Introduction Beginning with their seminal 2002 paper,
More informationMoral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania
Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 PrincipalAgent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically
More informationUnraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets
Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Nathaniel Hendren January, 2014 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that
More informationChapter 21: The Discounted Utility Model
Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal
More information6.254 : Game Theory with Engineering Applications Lecture 5: Existence of a Nash Equilibrium
6.254 : Game Theory with Engineering Applications Lecture 5: Existence of a Nash Equilibrium Asu Ozdaglar MIT February 18, 2010 1 Introduction Outline PricingCongestion Game Example Existence of a Mixed
More informationOn the Interaction and Competition among Internet Service Providers
On the Interaction and Competition among Internet Service Providers Sam C.M. Lee John C.S. Lui + Abstract The current Internet architecture comprises of different privately owned Internet service providers
More informationOligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry s output.
Topic 8 Chapter 13 Oligopoly and Monopolistic Competition Econ 203 Topic 8 page 1 Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry
More informationAdaptive Online Gradient Descent
Adaptive Online Gradient Descent Peter L Bartlett Division of Computer Science Department of Statistics UC Berkeley Berkeley, CA 94709 bartlett@csberkeleyedu Elad Hazan IBM Almaden Research Center 650
More informationImpact of QoS on Internet User Welfare
Impact of QoS on Internet User Welfare Galina Schwartz, Nikhil Shetty, and Jean Walrand Department of Electrical Engineering and Computer Sciences (EECS), University of California Berkeley, Cory Hall,
More informationECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE
ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE YUAN TIAN This synopsis is designed merely for keep a record of the materials covered in lectures. Please refer to your own lecture notes for all proofs.
More informationInsurance. Michael Peters. December 27, 2013
Insurance Michael Peters December 27, 2013 1 Introduction In this chapter, we study a very simple model of insurance using the ideas and concepts developed in the chapter on risk aversion. You may recall
More informationECON 312: Oligopolisitic Competition 1. Industrial Organization Oligopolistic Competition
ECON 312: Oligopolisitic Competition 1 Industrial Organization Oligopolistic Competition Both the monopoly and the perfectly competitive market structure has in common is that neither has to concern itself
More informationChapter 7. Sealedbid Auctions
Chapter 7 Sealedbid Auctions An auction is a procedure used for selling and buying items by offering them up for bid. Auctions are often used to sell objects that have a variable price (for example oil)
More information1.4 Hidden Information and Price Discrimination 1
1.4 Hidden Information and Price Discrimination 1 To be included in: Elmar Wolfstetter. Topics in Microeconomics: Industrial Organization, Auctions, and Incentives. Cambridge University Press, new edition,
More informationThe vertical differentiation model in the insurance market: costs structure and equilibria analysis
The vertical differentiation model in the insurance market: costs structure and equilibria analysis Denis V. Kuzyutin 1, Maria V. Nikitina, Nadezhda V. Smirnova and Ludmila N. Razgulyaeva 1 St.Petersburg
More informationLoad Balancing and Switch Scheduling
EE384Y Project Final Report Load Balancing and Switch Scheduling Xiangheng Liu Department of Electrical Engineering Stanford University, Stanford CA 94305 Email: liuxh@systems.stanford.edu Abstract Load
More information1 Nonzero sum games and Nash equilibria
princeton univ. F 14 cos 521: Advanced Algorithm Design Lecture 19: Equilibria and algorithms Lecturer: Sanjeev Arora Scribe: Economic and gametheoretic reasoning specifically, how agents respond to economic
More informationNotes V General Equilibrium: Positive Theory. 1 Walrasian Equilibrium and Excess Demand
Notes V General Equilibrium: Positive Theory In this lecture we go on considering a general equilibrium model of a private ownership economy. In contrast to the Notes IV, we focus on positive issues such
More informationPerformance of networks containing both MaxNet and SumNet links
Performance of networks containing both MaxNet and SumNet links Lachlan L. H. Andrew and Bartek P. Wydrowski Abstract Both MaxNet and SumNet are distributed congestion control architectures suitable for
More informationA Simple Characterization for TruthRevealing SingleItem Auctions
A Simple Characterization for TruthRevealing SingleItem Auctions Kamal Jain 1, Aranyak Mehta 2, Kunal Talwar 3, and Vijay Vazirani 2 1 Microsoft Research, Redmond, WA 2 College of Computing, Georgia
More informationI d Rather Stay Stupid: The Advantage of Having Low Utility
I d Rather Stay Stupid: The Advantage of Having Low Utility Lior Seeman Department of Computer Science Cornell University lseeman@cs.cornell.edu Abstract Motivated by cost of computation in game theory,
More information6.254 : Game Theory with Engineering Applications Lecture 2: Strategic Form Games
6.254 : Game Theory with Engineering Applications Lecture 2: Strategic Form Games Asu Ozdaglar MIT February 4, 2009 1 Introduction Outline Decisions, utility maximization Strategic form games Best responses
More informationA Game Theoretical Framework on Intrusion Detection in Heterogeneous Networks Lin Chen, Member, IEEE, and Jean Leneutre
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL 4, NO 2, JUNE 2009 165 A Game Theoretical Framework on Intrusion Detection in Heterogeneous Networks Lin Chen, Member, IEEE, and Jean Leneutre
More informationAn Introduction to Sponsored Search Advertising
An Introduction to Sponsored Search Advertising Susan Athey Market Design Prepared in collaboration with Jonathan Levin (Stanford) Sponsored Search Auctions Google revenue in 2008: $21,795,550,000. Hal
More informationA Token Pricing Scheme for Internet Services
A Token Pricing Scheme for Internet Services Dongmyung Lee 1, Jeonghoon Mo 2, Jean Walrand 3, and Jinwoo Park 1 1 Dept. of Industrial Engineering, Seoul National University, Seoul, Korea {leoleo333,autofact}@snu.ac.kr
More information17.6.1 Introduction to Auction Design
CS787: Advanced Algorithms Topic: Sponsored Search Auction Design Presenter(s): Nilay, Srikrishna, Taedong 17.6.1 Introduction to Auction Design The Internet, which started of as a research project in
More informationAn Economic Analysis of Multiple Internet QoS Channels
An Economic Analysis of Multiple Internet QoS Channels Dale O. Stahl Department of Economics The University of Texas Austin, TX 78712 Rui Dai Andrew B. Whinston MSIS Department The University of Texas
More information6.254 : Game Theory with Engineering Applications Lecture 1: Introduction
6.254 : Game Theory with Engineering Applications Lecture 1: Introduction Asu Ozdaglar MIT February 2, 2010 1 Introduction Optimization Theory: Optimize a single objective over a decision variable x R
More informationEquilibrium: Illustrations
Draft chapter from An introduction to game theory by Martin J. Osborne. Version: 2002/7/23. Martin.Osborne@utoronto.ca http://www.economics.utoronto.ca/osborne Copyright 1995 2002 by Martin J. Osborne.
More information8 Modeling network traffic using game theory
8 Modeling network traffic using game theory Network represented as a weighted graph; each edge has a designated travel time that may depend on the amount of traffic it contains (some edges sensitive to
More informationNetwork Traffic Modelling
University of York Dissertation submitted for the MSc in Mathematics with Modern Applications, Department of Mathematics, University of York, UK. August 009 Network Traffic Modelling Author: David Slade
More informationOnline Appendix for Student Portfolios and the College Admissions Problem
Online Appendix for Student Portfolios and the College Admissions Problem Hector Chade Gregory Lewis Lones Smith November 25, 2013 In this online appendix we explore a number of different topics that were
More information2.3 Convex Constrained Optimization Problems
42 CHAPTER 2. FUNDAMENTAL CONCEPTS IN CONVEX OPTIMIZATION Theorem 15 Let f : R n R and h : R R. Consider g(x) = h(f(x)) for all x R n. The function g is convex if either of the following two conditions
More informationA Simple Model of Price Dispersion *
Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price Dispersion
More informationSharing Online Advertising Revenue with Consumers
Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahooinc.com 2 Harvard University.
More information1 Uncertainty and Preferences
In this chapter, we present the theory of consumer preferences on risky outcomes. The theory is then applied to study the demand for insurance. Consider the following story. John wants to mail a package
More informationarxiv:1112.0829v1 [math.pr] 5 Dec 2011
How Not to Win a Million Dollars: A Counterexample to a Conjecture of L. Breiman Thomas P. Hayes arxiv:1112.0829v1 [math.pr] 5 Dec 2011 Abstract Consider a gambling game in which we are allowed to repeatedly
More informationTwo Papers on Internet Connectivity and Quality. Abstract
Two Papers on Internet Connectivity and Quality ROBERTO ROSON Dipartimento di Scienze Economiche, Università Ca Foscari di Venezia, Venice, Italy. Abstract I review two papers, addressing the issue of
More information2. Information Economics
2. Information Economics In General Equilibrium Theory all agents had full information regarding any variable of interest (prices, commodities, state of nature, cost function, preferences, etc.) In many
More informationFixed and Market Pricing for Cloud Services
NetEcon'212 1569559961 Fixed and Market Pricing for Cloud Services Vineet Abhishek Ian A. Kash Peter Key University of Illinois at UrbanaChampaign Microsoft Research Cambridge Microsoft Research Cambridge
More informationOPTIMAL CONTROL OF FLEXIBLE SERVERS IN TWO TANDEM QUEUES WITH OPERATING COSTS
Probability in the Engineering and Informational Sciences, 22, 2008, 107 131. Printed in the U.S.A. DOI: 10.1017/S0269964808000077 OPTIMAL CONTROL OF FLEXILE SERVERS IN TWO TANDEM QUEUES WITH OPERATING
More informationAlok Gupta. Dmitry Zhdanov
RESEARCH ARTICLE GROWTH AND SUSTAINABILITY OF MANAGED SECURITY SERVICES NETWORKS: AN ECONOMIC PERSPECTIVE Alok Gupta Department of Information and Decision Sciences, Carlson School of Management, University
More informationClosing the Price of Anarchy Gap in the Interdependent Security Game
Closing the Price of Anarchy Gap in the Interdependent Security Game Parinaz aghizadeh and Mingyan Liu Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, Michigan,
More informationTHE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING
THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING 1. Introduction The BlackScholes theory, which is the main subject of this course and its sequel, is based on the Efficient Market Hypothesis, that arbitrages
More informationA Pricing Mechanism for Intertemporal Bandwidth Sharing with Random Utilities and Resources
A Pricing Mechanism for Intertemporal Bandwidth Sharing with Random Utilities and Resources Alberto Pompermaier Department of Mathematics London School of Economics Houghton St. London WC2A 2AE England
More informationModeling Internet Security Investments
Modeling Internet Security Investments 1 The Case of Dealing with Information Uncertainty Ranjan Pal and Pan Hui University of Southern California, Deutsch Telekom Laboratories arxiv:1104.0594v1 [cs.cr]
More informationOptimal election of qualities in the presence of externalities
Optimal election of qualities in the presence of externalities Dolores Garcia Maria Tugores October 2002 Abstract In this paper we obtain the quality and the level of production that a certain sector would
More informationPrice competition with homogenous products: The Bertrand duopoly model [Simultaneous move price setting duopoly]
ECON9 (Spring 0) & 350 (Tutorial ) Chapter Monopolistic Competition and Oligopoly (Part ) Price competition with homogenous products: The Bertrand duopoly model [Simultaneous move price setting duopoly]
More informationChapter 7 Externalities
Chapter 7 Externalities Reading Essential reading Hindriks, J and G.D. Myles Intermediate Public Economics. (Cambridge: MIT Press, 2006) Chapter 7. Further reading Bator, F.M. (1958) The anatomy of market
More informationA Game Theoretic Approach to Traffic Flow Control. (MultiAgent Systems: Paper Project) May 2004
A Game Theoretic Approach to Traffic Flow Control (MultiAgent Systems: Paper Project) May 2004 Authors Jin Yu Enrico Faldini Programme Master in Artificial Intelligence Master in Artificial Intelligence
More informationLecture notes for Choice Under Uncertainty
Lecture notes for Choice Under Uncertainty 1. Introduction In this lecture we examine the theory of decisionmaking under uncertainty and its application to the demand for insurance. The undergraduate
More informationBidding Dynamics of Rational Advertisers in Sponsored Search Auctions on the Web
Proceedings of the International Conference on Advances in Control and Optimization of Dynamical Systems (ACODS2007) Bidding Dynamics of Rational Advertisers in Sponsored Search Auctions on the Web S.
More informationEquilibrium in Competitive Insurance Markets: An Essay on the Economic of Imperfect Information
Equilibrium in Competitive Insurance Markets: An Essay on the Economic of Imperfect Information By: Michael Rothschild and Joseph Stiglitz Presented by Benjamin S. Barber IV, Xiaoshu Bei, Zhi Chen, Shaiobi
More informationPricing Transmission
1 / 37 Pricing Transmission Quantitative Energy Economics Anthony Papavasiliou 2 / 37 Pricing Transmission 1 Equilibrium Model of Power Flow Locational Marginal Pricing Congestion Rent and Congestion Cost
More informationNetwork neutrality, usagebased pricing and service differentiation
Network neutrality, usagebased pricing and service differentiation George Kesidis, Penn State kesidis@engr.psu.edu G. de Veciana, U.T. Austin, and A. Das George Kesidis, PSU, CISS 2008 1 Outline Presentday
More informationOnline Ad Auctions. By Hal R. Varian. Draft: February 16, 2009
Online Ad Auctions By Hal R. Varian Draft: February 16, 2009 I describe how search engines sell ad space using an auction. I analyze advertiser behavior in this context using elementary price theory and
More informationCongestionDependent Pricing of Network Services
IEEE/ACM TRANSACTIONS ON NETWORKING, VOL 8, NO 2, APRIL 2000 171 CongestionDependent Pricing of Network Services Ioannis Ch Paschalidis, Member, IEEE, and John N Tsitsiklis, Fellow, IEEE Abstract We consider
More informationOn Stability Properties of Economic Solution Concepts
On Stability Properties of Economic Solution Concepts Richard J. Lipton Vangelis Markakis Aranyak Mehta Abstract In this note we investigate the stability of game theoretic and economic solution concepts
More informationWeek 7  Game Theory and Industrial Organisation
Week 7  Game Theory and Industrial Organisation The Cournot and Bertrand models are the two basic templates for models of oligopoly; industry structures with a small number of firms. There are a number
More informationProbability and Statistics
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2b  0 Probability and Statistics Kristel Van Steen, PhD 2 Montefiore Institute  Systems and Modeling GIGA  Bioinformatics ULg kristel.vansteen@ulg.ac.be
More informationConditions for Efficiency in Package Pricing
Conditions for Efficiency in Package Pricing Babu Nahata Department of Economics University of Louisville Louisville, Kentucky 40292, USA. email: nahata@louisville.edu and Serguei Kokovin and Evgeny Zhelobodko
More informationCost of Conciseness in Sponsored Search Auctions
Cost of Conciseness in Sponsored Search Auctions Zoë Abrams Yahoo!, Inc. Arpita Ghosh Yahoo! Research 2821 Mission College Blvd. Santa Clara, CA, USA {za,arpita,erikvee}@yahooinc.com Erik Vee Yahoo! Research
More informationWorking Paper Does retailer power lead to exclusion?
econstor www.econstor.eu Der OpenAccessPublikationsserver der ZBW LeibnizInformationszentrum Wirtschaft The Open Access Publication Server of the ZBW Leibniz Information Centre for Economics Rey, Patrick;
More informationQuasistatic evolution and congested transport
Quasistatic evolution and congested transport Inwon Kim Joint with Damon Alexander, Katy Craig and Yao Yao UCLA, UW Madison Hard congestion in crowd motion The following crowd motion model is proposed
More informationA Dutch Book for Group DecisionMaking?
A Dutch Book for Group DecisionMaking? Forthcoming in Benedikt Löwe, Eric Pacuit, JanWillem Romeijn (eds.) Foundations of the Formal Sciences VIReasoning about Probabilities and Probabilistic Reasoning.
More informationWhy do merchants accept payment cards?
Why do merchants accept payment cards? Julian Wright National University of Singapore Abstract This note explains why merchants accept expensive payment cards when merchants are Cournot competitors. The
More informationOligopoly: Cournot/Bertrand/Stackelberg
Outline Alternative Market Models Wirtschaftswissenschaften Humboldt Universität zu Berlin March 5, 2006 Outline 1 Introduction Introduction Alternative Market Models 2 Game, Reaction Functions, Solution
More information.4 120 +.1 80 +.5 100 = 48 + 8 + 50 = 106.
Chapter 16. Risk and Uncertainty Part A 2009, Kwan Choi Expected Value X i = outcome i, p i = probability of X i EV = pix For instance, suppose a person has an idle fund, $100, for one month, and is considering
More informationConvex analysis and profit/cost/support functions
CALIFORNIA INSTITUTE OF TECHNOLOGY Division of the Humanities and Social Sciences Convex analysis and profit/cost/support functions KC Border October 2004 Revised January 2009 Let A be a subset of R m
More informationComputational Learning Theory Spring Semester, 2003/4. Lecture 1: March 2
Computational Learning Theory Spring Semester, 2003/4 Lecture 1: March 2 Lecturer: Yishay Mansour Scribe: Gur Yaari, Idan Szpektor 1.1 Introduction Several fields in computer science and economics are
More informationOn the Existence of Nash Equilibrium in General Imperfectly Competitive Insurance Markets with Asymmetric Information
analysing existence in general insurance environments that go beyond the canonical insurance paradigm. More recently, theoretical and empirical work has attempted to identify selection in insurance markets
More informationThis article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
IEEE/ACM TRANSACTIONS ON NETWORKING 1 A Greedy Link Scheduler for Wireless Networks With Gaussian MultipleAccess and Broadcast Channels Arun Sridharan, Student Member, IEEE, C Emre Koksal, Member, IEEE,
More informationBuyer Search Costs and Endogenous Product Design
Buyer Search Costs and Endogenous Product Design Dmitri Kuksov kuksov@haas.berkeley.edu University of California, Berkeley August, 2002 Abstract In many cases, buyers must incur search costs to find the
More informationA CournotNash Bertrand Game Theory Model of a ServiceOriented Internet with Price and Quality Competition Among Network Transport Providers
of a ServiceOriented Internet with Price and Quality Competition Among Network Transport Providers Anna Nagurney 1 Tilman Wolf 2 1 Isenberg School of Management University of Massachusetts Amherst, Massachusetts
More informationLecture 6: Price discrimination II (Nonlinear Pricing)
Lecture 6: Price discrimination II (Nonlinear Pricing) EC 105. Industrial Organization. Fall 2011 Matt Shum HSS, California Institute of Technology November 14, 2012 EC 105. Industrial Organization. Fall
More informationAbout the inverse football pool problem for 9 games 1
Seventh International Workshop on Optimal Codes and Related Topics September 61, 013, Albena, Bulgaria pp. 15133 About the inverse football pool problem for 9 games 1 Emil Kolev Tsonka Baicheva Institute
More informationCPC/CPA Hybrid Bidding in a Second Price Auction
CPC/CPA Hybrid Bidding in a Second Price Auction Benjamin Edelman Hoan Soo Lee Working Paper 09074 Copyright 2008 by Benjamin Edelman and Hoan Soo Lee Working papers are in draft form. This working paper
More informationCapacity Management and Equilibrium for Proportional QoS
IEEE/ACM TRANSACTIONS ON NETWORKING 1 Capacity Management and Equilibrium for Proportional QoS Ishai Menache and Nahum Shimkin, Senior Member, IEEE Abstract Differentiated services architectures are scalable
More informationWorking Paper Series
RGEA Universidade de Vigo http://webs.uvigo.es/rgea Working Paper Series A Market Game Approach to Differential Information Economies Guadalupe Fugarolas, Carlos HervésBeloso, Emma Moreno García and
More informationCoordination in Network Security Games
Coordination in Network Security Games Marc Lelarge INRIA  ENS Paris, France Email: marc.lelarge@ens.fr Abstract Malicious softwares or malwares for short have become a major security threat. While originating
More informationOnline Appendix Feedback Effects, Asymmetric Trading, and the Limits to Arbitrage
Online Appendix Feedback Effects, Asymmetric Trading, and the Limits to Arbitrage Alex Edmans LBS, NBER, CEPR, and ECGI Itay Goldstein Wharton Wei Jiang Columbia May 8, 05 A Proofs of Propositions and
More informationModeling Internet Security Investments Tackling Topological Information Uncertainty
Modeling Internet Security Investments Tackling Topological Information Uncertainty Ranjan Pal Department of Computer Science University of Southern California, USA Joint Work with Pan Hui Deutsch Telekom
More informationLecture 11: Sponsored search
Computational Learning Theory Spring Semester, 2009/10 Lecture 11: Sponsored search Lecturer: Yishay Mansour Scribe: Ben Pere, Jonathan Heimann, Alon Levin 11.1 Sponsored Search 11.1.1 Introduction Search
More information10 Evolutionarily Stable Strategies
10 Evolutionarily Stable Strategies There is but a step between the sublime and the ridiculous. Leo Tolstoy In 1973 the biologist John Maynard Smith and the mathematician G. R. Price wrote an article in
More informationOPRE 6201 : 2. Simplex Method
OPRE 6201 : 2. Simplex Method 1 The Graphical Method: An Example Consider the following linear program: Max 4x 1 +3x 2 Subject to: 2x 1 +3x 2 6 (1) 3x 1 +2x 2 3 (2) 2x 2 5 (3) 2x 1 +x 2 4 (4) x 1, x 2
More informationUniversidad de Montevideo Macroeconomia II. The RamseyCassKoopmans Model
Universidad de Montevideo Macroeconomia II Danilo R. Trupkin Class Notes (very preliminar) The RamseyCassKoopmans Model 1 Introduction One shortcoming of the Solow model is that the saving rate is exogenous
More informationDecision Theory. 36.1 Rational prospecting
36 Decision Theory Decision theory is trivial, apart from computational details (just like playing chess!). You have a choice of various actions, a. The world may be in one of many states x; which one
More information3. Reaction Diffusion Equations Consider the following ODE model for population growth
3. Reaction Diffusion Equations Consider the following ODE model for population growth u t a u t u t, u 0 u 0 where u t denotes the population size at time t, and a u plays the role of the population dependent
More informationAn Asymptotically Optimal Scheme for P2P File Sharing
An Asymptotically Optimal Scheme for P2P File Sharing Panayotis Antoniadis Costas Courcoubetis Richard Weber Athens University of Economics and Business Athens University of Economics and Business Centre
More informationDesigning Incentives in Online Collaborative Environments 1
Designing Incentives in Online Collaborative Environments 1 Yoram Bachrach, Vasilis Syrgkanis, and Milan Vojnović November 2012 Technical Report MSRTR2012115 Microsoft Research Microsoft Corporation
More informationForthcoming in Research Papers Series, SU HSE, Research in Economics and Finance, May 2010
Forthcoming in Research Papers Series, SU HSE, Research in Economics and Finance, May 2010 How Does Income Inequality Affect Market Outcomes in Vertically Differentiated Markets? Anna V. Yurko State University
More informationFairness in Routing and Load Balancing
Fairness in Routing and Load Balancing Jon Kleinberg Yuval Rabani Éva Tardos Abstract We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria
More informationOn the optimality of optimal income taxation
Preprints of the Max Planck Institute for Research on Collective Goods Bonn 2010/14 On the optimality of optimal income taxation Felix Bierbrauer M A X P L A N C K S O C I E T Y Preprints of the Max Planck
More informationSharing Online Advertising Revenue with Consumers
Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahooinc.com 2 Harvard University.
More informationK 1 < K 2 = P (K 1 ) P (K 2 ) (6) This holds for both American and European Options.
Slope and Convexity Restrictions and How to implement Arbitrage Opportunities 1 These notes will show how to implement arbitrage opportunities when either the slope or the convexity restriction is violated.
More informationON PRICE CAPS UNDER UNCERTAINTY
ON PRICE CAPS UNDER UNCERTAINTY ROBERT EARLE CHARLES RIVER ASSOCIATES KARL SCHMEDDERS KSMMEDS, NORTHWESTERN UNIVERSITY TYMON TATUR DEPT. OF ECONOMICS, PRINCETON UNIVERSITY APRIL 2004 Abstract. This paper
More information20 Selfish Load Balancing
20 Selfish Load Balancing Berthold Vöcking Abstract Suppose that a set of weighted tasks shall be assigned to a set of machines with possibly different speeds such that the load is distributed evenly among
More informationTruthful and NonMonetary Mechanism for Direct Data Exchange
Truthful and NonMonetary Mechanism for Direct Data Exchange IHong Hou, YuPin Hsu and Alex Sprintson Department of Electrical and Computer Engineering Texas A&M University {ihou, yupinhsu, spalex}@tamu.edu
More informationECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2015
ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2015 These notes have been used before. If you can still spot any errors or have any suggestions for improvement, please let me know. 1
More informationEconomics 165 Winter 2002 Problem Set #2
Economics 165 Winter 2002 Problem Set #2 Problem 1: Consider the monopolistic competition model. Say we are looking at sailboat producers. Each producer has fixed costs of 10 million and marginal costs
More information