Nonconvergence to saddle boundary points under perturbed reinforcement learning

Georgios C. Chasparis, Jeff S. Shamma, Anders Rantzer

Research output: Contribution to journalArticlepeer-review


For several reinforcement learning models in strategic-form games, convergence to action profiles that are not Nash equilibria may occur with positive probability under certain conditions on the payoff function. In this paper, we explore how an alternative reinforcement learning model, where the strategy of each agent is perturbed by a strategy-dependent perturbation (or mutations) function, may exclude convergence to non-Nash pure strategy profiles. This approach extends prior analysis on reinforcement learning in games that addresses the issue of convergence to saddle boundary points. It further provides a framework under which the effect of mutations can be analyzed in the context of reinforcement learning.

Original languageEnglish (US)
Pages (from-to)667-699
Number of pages33
JournalInternational Journal of Game Theory
Issue number3
StatePublished - Aug 31 2015
Externally publishedYes


  • Learning in games
  • Reinforcement learning
  • Replicator dynamics

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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