Topological Price of Anarchy Bounds for Clustering Games on Networks

Kleer, Pieter; Schäfer, Guido

doi:10.1007/978-3-030-35389-6_18

Cited by 2 publications

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References 38 publications

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“…There exist many generalizations of max cut games, see, e.g.,[34] and references therein, for which it might also be interesting to study the logit dynamics.…”

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confidence: 99%

Sampling from the Gibbs Distribution in Congestion Games

Kleer¹

2021

Preprint

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Logit dynamics is a form of randomized game dynamics where players have a bias towards strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converges to the so-called Gibbs distribution over the set of all strategy profiles, when interpreted as a Markov chain. In general, logit dynamics might converge slowly to the Gibbs distribution, but beyond that, not much is known about their algorithmic aspects, nor that of the Gibbs distribution. In this work, we are interested in the following two questions for congestion games: i) Is there an efficient algorithm for sampling from the Gibbs distribution? ii) If yes, do there also exist natural randomized dynamics that converges quickly to the Gibbs distribution?We first study these questions in extension parallel congestion games, a well-studied special case of symmetric network congestion games. As our main result, we show that there is a simple variation on the logit dynamics (in which we in addition are also allowed to randomly interchange the strategies of two players) that converges quickly to the Gibbs distribution in such games. This answers both questions above affirmatively. We also address the first question for the class of so-called capacitated k-uniform congestion games.To prove our results, we rely on the recent breakthrough work of Anari, Liu, Oveis-Gharan and Vinzant (2019) concerning the approximate sampling of the base of a matroid according to strongly log-concave probability distribution.

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“…There exist many generalizations of max cut games, see, e.g.,[34] and references therein, for which it might also be interesting to study the logit dynamics.…”

mentioning

confidence: 99%

Sampling from the Gibbs Distribution in Congestion Games

Kleer¹

2021

Preprint

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Topological Bounds on the Price of Anarchy of Clustering Games on Networks

Kleer,

Schäfer

2023

ACM Trans. Econ. Comput.

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We consider clustering games in which the players are embedded into a network and want to coordinate (or anti-coordinate) their strategy with their neighbors. The goal of a player is to choose a strategy that maximizes her utility given the strategies of her neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy: A large inefficiency between the total utility generated in centralized outcomes and equilibrium outcomes in which players selfishly maximize their utility. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding worst-case Price of Anarchy bounds. More specifically, depending on the type of clustering game, our bounds reveal that the Price of Anarchy depends on the maximum subgraph density or the maximum degree of the graph. Among others, these bounds enable us to derive bounds on the Price of Anarchy for clustering games on Erdős-Rényi random graphs. Depending on the graph density, these bounds stand in stark contrast to the known worst-case Price of Anarchy bounds. Additionally, we also characterize the set of distribution rules that guarantee the existence of a pure Nash equilibrium or the convergence of best-response dynamics. These results are of a similar spirit as the work of Gopalakrishnan et al. [19] and complement work of Anshelevich and Sekar [4].

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Topological Price of Anarchy Bounds for Clustering Games on Networks

Cited by 2 publications

References 38 publications

Sampling from the Gibbs Distribution in Congestion Games

Sampling from the Gibbs Distribution in Congestion Games

Topological Bounds on the Price of Anarchy of Clustering Games on Networks

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