TY - GEN

T1 - Bottleneck congestion games with logarithmic price of anarchy

AU - Kannan, Rajgopal

AU - Busch, Costas

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010

Y1 - 2010

N2 - We study bottleneck congestion games where the social cost is determined by the worst congestion on any resource. In the literature, bottleneck games assume player utility costs determined by the worst congested resource in their strategy. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the number of resources. In order to obtain smaller price of anarchy we introduce exponential bottleneck games, where the utility costs of the players are exponential functions of their congestions. In particular, the delay function for any resource r is , where C r denotes the number of players that use r, and is an integer constant. We find that exponential bottleneck games are very efficient and give the following bound on the price of anarchy: O(log|R|), where R is the set of resources. This price of anarchy is tight, since we demonstrate a game with price of anarchy Ω(log|R|). We obtain our tight bounds by using two novel proof techniques: transformation, which we use to convert arbitrary games to simpler games, and expansion, which we use to bound the price of anarchy in a simpler game.

AB - We study bottleneck congestion games where the social cost is determined by the worst congestion on any resource. In the literature, bottleneck games assume player utility costs determined by the worst congested resource in their strategy. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the number of resources. In order to obtain smaller price of anarchy we introduce exponential bottleneck games, where the utility costs of the players are exponential functions of their congestions. In particular, the delay function for any resource r is , where C r denotes the number of players that use r, and is an integer constant. We find that exponential bottleneck games are very efficient and give the following bound on the price of anarchy: O(log|R|), where R is the set of resources. This price of anarchy is tight, since we demonstrate a game with price of anarchy Ω(log|R|). We obtain our tight bounds by using two novel proof techniques: transformation, which we use to convert arbitrary games to simpler games, and expansion, which we use to bound the price of anarchy in a simpler game.

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U2 - 10.1007/978-3-642-16170-4_20

DO - 10.1007/978-3-642-16170-4_20

M3 - Conference contribution

AN - SCOPUS:78649534215

SN - 3642161693

SN - 9783642161698

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 222

EP - 233

BT - Algorithmic Game Theory - Third International Symposium, SAGT 2010, Proceedings

T2 - 3rd International Symposium on Algorithmic Game Theory, SAGT 2010

Y2 - 18 October 2010 through 20 October 2010

ER -