The price of anarchy and stability in general noisy best-response dynamics

Penna, Paolo

doi:10.1007/s00182-017-0601-y

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…For an exposition of the notion of logit equilibrium, and more related work, we refer to the survey article of Ferraioli [20] and references therein. There are also various results addressing the inefficiency of 'long-term' equilibria in the context of logit dynamics, see, e.g., the works of Asadpour and Saberi [7], Mamageishvili and Penna [36] and Penna [44].…”

Section: Further Related Workmentioning

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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Section: Further Related Workmentioning

confidence: 99%

Sampling from the Gibbs Distribution in Congestion Games

Kleer¹

2021

Preprint

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“…In the original logit dynamics by [6,7], where one randomly chosen player moves at a time, they essentially rest on a subset of potential minimizers. When the players' schedule is relaxed, this property is lost and additional conditions on the game are required [1,10,2,18,26]. Our independent better-response dynamics can be seen as an analog of the independent dynamics of [1] for logit response.…”

Section: Related Workmentioning

confidence: 99%

Independent Lazy Better-Response Dynamics on Network Games

Penna

Viennot

2019

Lecture Notes in Computer Science

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We study an independent best-response dynamics on network games in which the nodes (players) decide to revise their strategies independently with some probability. We provide several bounds on the convergence time to an equilibrium as a function of this probability, the degree of the network, and the potential of the underlying games. These dynamics are somewhat more suitable for distributed environments than the classical better-and best-response dynamics where players revise their strategies "sequentially", i.e., no two players revise their strategies simultaneously.

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Sampling from the Gibbs Distribution in Congestion Games

Kleer

2023

Mathematics of OR

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Logit dynamics is a form of randomized game dynamics in which players have a bias toward strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converge to the so-called Gibbs distribution over the set of all strategy profiles when interpreted as a Markov chain. In general, logit dynamics can converge slowly to the Gibbs distribution, but beyond that, not much is known about its 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, does there also exist natural randomized dynamics that converge 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 that converges quickly to the Gibbs distribution in such games. We also address the first question for the class of so-called capacitated uniform congestion games and the second question for max cut games played on a complete graph. To prove our results, we rely on the recent breakthrough work of Anari et al. (2019) regarding the approximate sampling of a base of a matroid according to a strongly log-concave probability distribution.

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The price of anarchy and stability in general noisy best-response dynamics

Cited by 3 publications

References 28 publications

Sampling from the Gibbs Distribution in Congestion Games

Sampling from the Gibbs Distribution in Congestion Games

Independent Lazy Better-Response Dynamics on Network Games

Sampling from the Gibbs Distribution in Congestion Games

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