Large deviations and stochastic stability in the small noise double limit

Sandholm, William H.; Staudigl, Mathias

doi:10.3982/te1905

Cited by 31 publications

(38 citation statements)

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“…Our framework also differs fromSandholm and Staudigl (2015), who studied the rate at which certain types of stochastic learning dynamics converge to the stochastically stable equilibrium. In games with multiple equilibria, the convergence time can also grow exponentially with N.8 In a similar spirit,Pradelski (2015) showed that by introducing aggregate shocks to a twosided matching market, the convergence time becomes polynomial in the number of players, rather than exponential.…”

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confidence: 99%

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Arieli

Young²

2016

Econometrica

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We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium.

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confidence: 99%

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Arieli

Young²

2016

Econometrica

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“…There are strong reasons to expect this double limit to be analytically tractable. In Sandholm and Staudigl (2016), we study the reverse order of limits, under which the noise level η is first taken to zero, and then the population size N to infinity. For this order of limits, we show that large deviations properties are determined by the solutions to piecewise linear control problems, and that these problems can be solved analytically.…”

Section: Discussionmentioning

confidence: 99%

“…Since the logit protocol is parameterized by a noise level and since clever payoff evaluation is used, this example satisfies the assumptions of our analysis of the small noise double limit inSandholm and Staudigl (2016).…”

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confidence: 99%

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Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics

Sandholm

Staudigl²

2018

Mathematics of OR

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We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of decay of the probability that the sample path of the evolutionary process lies in a prespecified set as the population size approaches infinity. We use these results to describe excursion rates and stationary distribution asymptotics in settings where the mean dynamic admits a globally attracting state, and we compute these rates explicitly for the case of logit choice in potential games. * We thank Michel Benaïm for extensive discussions about this paper and related topics, and two anonymous referees and an Associate Editor for helpful comments.

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“…To find the cost of least cost transitions between conventions, Sandholm and Staudigl [304], building on Staudigl [337], show that, as a finite population grows large, transition costs can be approximated by solutions to continuous optimal control problems. They illustrate the method by analyzing stochastic stability under logit choice of three strategy coordination games that satisfy the marginal bandwagon property of (Kandori and Rob [190]), under which, for strategies i, j, k, i / ∈ {j, k},…”

Section: Least Cost Transition Pathsmentioning

confidence: 99%

Evolutionary Game Theory: A Renaissance

Newton

2018

Games

173

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Economic agents are not always rational or farsighted and can make decisions according to simple behavioral rules that vary according to situation and can be studied using the tools of evolutionary game theory. Furthermore, such behavioral rules are themselves subject to evolutionary forces. Paying particular attention to the work of young researchers, this essay surveys the progress made over the last decade towards understanding these phenomena, and discusses open research topics of importance to economics and the broader social sciences.

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Large deviations and stochastic stability in the small noise double limit

Cited by 31 publications

References 38 publications

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics

Evolutionary Game Theory: A Renaissance

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