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13
Efficiency of ScalarParameterized Mechanisms
"... We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communica ..."
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Cited by 14 (2 self)
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We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks; in particular, we restrict attention to mechanisms where users are restricted to onedimensional strategy spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate. We study the worstcase efficiency loss (ratio of the utility associated with a Nash equilibrium to the maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price differentiation is permitted; using an adaptation of the VickreyClarkeGroves class of mechanisms, we construct a class of mechanisms with onedimensional strategy spaces where Nash equilibria are fully efficient. These mechanisms are shown to be fully efficient even in general convex environments, under reasonable assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually improve the efficiency guarantee.
The price of anarchy of serial, average, and incremental cost sharing
 FORTHCOMING, ECONOMIC THEORY
, 2007
"... Users share an increasing marginal cost technology. A cost sharing method charges non negative cost shares covering costs. We look at the worst surplus (relative to the efficient surplus) in a Nash equilibrium of the demand game, where the minimum is taken over all convex preferences quasilinear in ..."
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Cited by 11 (3 self)
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Users share an increasing marginal cost technology. A cost sharing method charges non negative cost shares covering costs. We look at the worst surplus (relative to the efficient surplus) in a Nash equilibrium of the demand game, where the minimum is taken over all convex preferences quasilinear in cost shares. We compare average cost pricing and serial cost sharing, two budgetbalanced methods, and incremental cost sharing, a method collecting a budget surplus, that we count as a welfare loss. For any convex cost function, the average cost and serial methods guarantee a (relative) surplus no less than 1, where n is the number of n users. For some cost functions incremental cost sharing guarantees no positive gain. With quadratic costs, the surplus guaranteed by serial cost sharing is θ ( 1
Design of price mechanisms for network resource allocation via price of anarchy. Mimeo
, 2005
"... We study the design of price mechanisms for communication network problems in which a user’s utility depends on the amount of flow she sends through the network, and the congestion on each link depends on the total traffic flows over it. The price mechanisms are characterized by a set of axioms that ..."
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Cited by 10 (0 self)
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We study the design of price mechanisms for communication network problems in which a user’s utility depends on the amount of flow she sends through the network, and the congestion on each link depends on the total traffic flows over it. The price mechanisms are characterized by a set of axioms that have been adopted in the costsharing games, and we search for the price mechanisms that provide the minimum price of anarchy. We show that, given the nondecreasing and concave utilities of users and the convex quadratic congestion costs in each link, if the price mechanism cannot depend on utility functions, the best achievable price of anarchy is 4(3 − 2 √ 2) ≈ 31.4%. Thus, the popular marginal cost pricing with price of anarchy less than 1/3 ≈ 33.3 % is nearly optimal. We also investigate the scenario in which the price mechanisms can be made contingent on the users ’ preference profile while such information is available. Mathematics Subject Classification (MSC): 90B18 1
Rankingbased Optimal Resource Allocation in PeertoPeer Networks
"... Abstract—This paper presents a theoretic framework of optimal resource allocation and admission control for peertopeer networks. Peer’s behavioral rankings are incorporated into the resource allocation and admission control to provide differentiated services and even to block peers with bad ranking ..."
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Cited by 4 (0 self)
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Abstract—This paper presents a theoretic framework of optimal resource allocation and admission control for peertopeer networks. Peer’s behavioral rankings are incorporated into the resource allocation and admission control to provide differentiated services and even to block peers with bad rankings. These peers may be freeriders or suspicious attackers. A peer improves her ranking by contributing resources to the P2P system or deteriorates her ranking by consuming services. Therefore, the rankingbased resource allocation provides necessary incentives for peers to contribute their resources to the P2P systems. We define a utility function which captures the best wish for the source peer to serve competing peers, who request services from the source peer. Although the utility function is convex, Harsanyitype social welfare functions are devised to obtain a unique optimal resource allocation that achieves maxmin fairness. The parameters used in our model can be derived from the nature of the services or chosen by the source peer. No private information is required to reveal from individual peers. This prevents selfish peers to play the system strategically and cheat the resource allocation mechanism for their own benefits. The resource allocation and admission control are fully distributed and linearly scalable. I.
The price of anarchy of serial cost sharing and other methods Working paper
, 2005
"... Users share an increasing marginal cost technology. A method charges non negative cost shares covering costs. We look at the worst surplus (relative to the efficient surplus) in a Nash equilibrium of the demand game, where the minimum is taken over all convex preferences quasilinear in cost shares. ..."
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Cited by 4 (2 self)
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Users share an increasing marginal cost technology. A method charges non negative cost shares covering costs. We look at the worst surplus (relative to the efficient surplus) in a Nash equilibrium of the demand game, where the minimum is taken over all convex preferences quasilinear in cost shares. We compare two budgetbalanced methods, average cost pricing and serial cost sharing, and two methods collecting a budget surplus, marginal cost pricing and incremental cost sharing. In the latter case we count the budget surplus as a loss. For any convex cost function, the average cost and serial methods guarantee a (relative) surplus no less than 1,wherenis the number of users. n Neither marginal cost pricing, nor incremental cost sharing guarantees any positive gain. With quadratic costs, the surplus guaranteed by serial cost sharing is O ( 1 log n) for the three other methods. This generalizes if the marginal cost is convex or concave, and its elasticity is bounded. Key words: price of anarchy, cost sharing, average cost, serial cost, marginal cost, incremental cost. Acknowledgments Support from the NSF, under grant SES0414543, is gratefully acknowledged.The comments of seminar particiants at Microsoft Research have been very helpful.
The Price of Anarchy in a Network Pricing Game
"... We analyze a game theoretic model of competing network service providers that strategically price their service in the presence of elastic user demand. Demand is elastic in that it diminishes both with higher prices and congestion. The model we study is based on a model first proposed and studied b ..."
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Cited by 3 (1 self)
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We analyze a game theoretic model of competing network service providers that strategically price their service in the presence of elastic user demand. Demand is elastic in that it diminishes both with higher prices and congestion. The model we study is based on a model first proposed and studied by Acemoglu and Ozdaglar and later extended by Hayrapetyan, Tardos, and Wexler to consider elastic user demand. We consider the price of anarchy, which we define as the ratio of the social welfare of the system when a social planner chooses link prices versus the social welfare attained when link owners choose the link prices selfishly. Ozdaglar has recently shown that the price of anarchy in the network pricing game with elastic demand is no more than 1.5. We have independently derived the same result. In contrast to Ozdaglar’s proof based on mathematical programming techniques, our proof uses linear algebra and is motivated by making an analogy to a network of resistors. Our technique is useful because it provides an intuitive explanation for the result, as well as providing a framework from which to derive extensions to the result.
Price of anarchy of cognitive mac games
 in IEEE Global Communications Conference (ICC
, 2009
"... Abstract — In this paper, we model and analyze the interactions between secondary users in a spectrum overlay cognitive system as a cognitive MAC game. In this game, each secondary user can sense (and transmit) one of several channels, the availability of each channel is determined by the activity o ..."
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Cited by 2 (1 self)
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Abstract — In this paper, we model and analyze the interactions between secondary users in a spectrum overlay cognitive system as a cognitive MAC game. In this game, each secondary user can sense (and transmit) one of several channels, the availability of each channel is determined by the activity of the corresponding primary user. We show that this game belongs to the class of congestion game and thus there exists at least one Nash Equilibrium. We focus on analyzing the worst case efficiency loss (i.e., price of anarchy) at any Nash Equilibrium of such a game. Closedform expressions of price of anarchy are derived for both symmetric and asymmetric games, with arbitrary channel and user heterogeneity. Several insights are also derived in terms of how to design a better cognitive radio system with less severe efficiency loss. I. BACKGROUND AND CONTRIBUTIONS
Parameterized Supply Function Bidding: Equilibrium and Welfare
, 2007
"... Motivated by market design for electric power systems, we consider a model where a finite number of producers compete to meet an infinitely divisible but inelastic demand for the product. Each firm is characterized by a production cost that is convex in the output produced, and firms act as profit m ..."
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Cited by 2 (0 self)
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Motivated by market design for electric power systems, we consider a model where a finite number of producers compete to meet an infinitely divisible but inelastic demand for the product. Each firm is characterized by a production cost that is convex in the output produced, and firms act as profit maximizers. We consider a uniform price market design that uses supply function bidding [22]: firms declare the amount they would supply at any positive price, and a single price is chosen to clear the market. We are interested in evaluating the impact of price anticipating behavior both on the allocative efficiency of the market, and on the prices seen at equilibrium. We show that by restricting the strategy space of the firms to parameterized supply functions, we can provide upper bounds on both the inflation of aggregate cost at the Nash equilibrium relative to the socially optimal level, as well as the markup of the Nash equilibrium price above the competitive level: as long as N> 2 firms are competing, these quantities are both upper bounded by 1 + 1/(N − 2). This result holds even in the presence of asymmetric cost structure across firms. We also discuss several extensions, generalizations, and related issues.