On the Equilibria of Alternating Move Games

Roth, Aaron; Balcan, Maria Florina; Kalai, Adam Tauman; Mansour, Yishay

doi:10.1137/1.9781611973075.66

Cited by 10 publications

(20 citation statements)

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“…As for approximation schemes, the only result we are aware [36] of is the observation that the values of BW-games can be approximated within an absolute error of ε in polynomial-time, if all rewards are in the range [−1, 1]. This follows immediately from truncating the rewards and using any of the known pseudo-polynomial algorithms [21,35,40].…”

Section: Previous Resultsmentioning

confidence: 99%

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Approximation Schemes for Stochastic Mean Payoff Games with Perfect Information and Few Random Positions

et al. 2017

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Section: Previous Resultsmentioning

confidence: 99%

“…In this paper, we extend the absolute FPTAS for BW-games [36] in two directions. First, we allow a constant number of random positions, and, second, we derive an FPTAS with a relative approximation error.…”

Section: Our Resultsmentioning

confidence: 99%

Approximation Schemes for Stochastic Mean Payoff Games with Perfect Information and Few Random Positions

et al. 2017

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“…A natural question is whether we could efficiently approximate the value in MPG with no restrictions on the weights. The next theorem shows that a generalization of the positive approximation result in [15] on MPG with arbitrary (rational) weights would indeed provide a polynomial time exact solution to the MPG value problem.…”

Section: Approximate Solutions For Mpgmentioning

confidence: 88%

“…The works in [9,3] define a randomized algorithm which is both subexponential and pseudopolynomial. Recently, the authors of [15,4] show that the pseudopolynomial procedures in [18,13,12] can be used to design (fully) polynomial value approximation schemes for certain classes of meanpayoff games: namely, mean-payoff games with positive (integer) weights or rational weights with absolute value less or equal to 1. In this paper, we consider the problem of extending such positive approximation results for general mean-payoff games, i.e.…”

Section: Problems Algorithmsmentioning

confidence: 99%

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A note on the approximation of mean-payoff games

Gentilini

2014

Information Processing Letters

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Abstract. We consider the problem of designing approximation schemes for the values of mean-payoff games. It was recently shown that (1) mean-payoff with rational weights scaled on [−1, 1] admit additive fully-polynomial approximation schemes, and (2) mean-payoff games with positive weights admit relative fully-polynomial approximation schemes. We show that the problem of designing additive/relative approximation schemes for general mean-payoff games (i.e. with no constraint on their edge-weights) is P-time equivalent to determining their exact solution.

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Mixing Time and Stationary Expected Social Welfare of Logit Dynamics

Auletta

Ferraioli

Pasquale

et al. 2010

Algorithmic Game Theory

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We study "logit dynamics" [Blume, Games and Economic Behavior, 1993] for strategic games. This dynamics works as follows: at every stage of the game a player is selected uniformly at random and she plays according to a "noisy" best-response where the noise level is tuned by a parameter $\beta$. Such a dynamics defines a family of ergodic Markov chains, indexed by $\beta$, over the set of strategy profiles. We believe that the stationary distribution of these Markov chains gives a meaningful description of the long-term behavior for systems whose agents are not completely rational. Our aim is twofold: On the one hand, we are interested in evaluating the performance of the game at equilibrium, i.e. the expected social welfare when the strategy profiles are random according to the stationary distribution. On the other hand, we want to estimate how long it takes, for a system starting at an arbitrary profile and running the logit dynamics, to get close to its stationary distribution; i.e., the "mixing time" of the chain. In this paper we study the stationary expected social welfare for the 3-player CK game, for 2-player coordination games, and for two simple $n$-player games. For all these games, we also give almost tight upper and lower bounds on the mixing time of logit dynamics. Our results show two different behaviors: in some games the mixing time depends exponentially on $\beta$, while for other games it can be upper bounded by a function independent of $\beta$.Comment: 28 page

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On the Equilibria of Alternating Move Games

Cited by 10 publications

References 0 publications

Approximation Schemes for Stochastic Mean Payoff Games with Perfect Information and Few Random Positions

Approximation Schemes for Stochastic Mean Payoff Games with Perfect Information and Few Random Positions

A note on the approximation of mean-payoff games

Mixing Time and Stationary Expected Social Welfare of Logit Dynamics

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