Large Deviations And Stochastic Stability In Population Games

M. Staudigl*, S. Arigapudi, W.H. Sandholm

*Corresponding author for this work

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Abstract

In this article we review a model of stochastic evolution under general noisy best-response protocols, allowing the probabilities of suboptimal choices to depend on their payoff consequences. We survey the methods developed by the authors which allow for a quantitative analysis of these stochastic evolutionary game dynamics. We start with a compact survey of techniques designed to study the long run behavior in the small noise double limit (SNDL). In this regime we let the noise level in agents' decision rules to approach zero, and then the population size is formally taken to infinity. This iterated limit strategy yields a family of deterministic optimal control problems which admit an explicit analysis in many instances. We then move in by describing the main steps to analyze stochastic evolutionary game dynamics in the large population double limit (LPDL). This regime refers to the iterated limit in which first the population size is taken to infinity and then the noise level in agents' decisions vanishes. The mathematical analysis of LPDL relies on a sample-path large deviations principle for a family of Markov chains on compact polyhedra. In this setting we formulate a set of conjectures and open problems which give a clear direction for future research activities.
Original languageEnglish
Pages (from-to)569-595
Number of pages27
JournalJournal of Dynamics and Games
Volume9
Issue number4
Early online date1 Oct 2020
DOIs
Publication statusPublished - Oct 2022

Keywords

  • large deviations
  • Hamilton-Jacobi equations
  • state-constrained optimal control
  • Markov chains
  • DETERMINISTIC APPROXIMATION
  • EVOLUTIONARY DYNAMICS
  • POTENTIAL GAMES
  • EQUILIBRIUM
  • STRATEGIES
  • ALGORITHMS

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