Reinforcement Learning in Repeated Interaction Games

Jonathan Bendor, Dilip Mookherjee, Debraj Ray

    Research output: Contribution to journalArticlepeer-review


    We study long run implications of reinforcement learning when two players repeatedly interact with one another over multiple rounds to play a finite action game. Within each round, the players play the game many successive times with a fixed set of aspirations used to evaluate payoff experiences as successes or failures. The probability weight on successful actions is increased, while failures result in players trying alternative actions in subsequent rounds. The learning rule is supplemented by small amounts of inertia and random perturbations to the states of players. Aspirations are adjusted across successive rounds on the basis of the discrepancy between the average payoff and aspirations in the most recently concluded round. We define and characterize pure steady states of this model, and establish convergence to these under appropriate conditions. Pure steady states are shown to be individually rational, and are either Pareto-efficient or a protected Nash equilibrium of the stage game. Conversely, any Pareto-efficient and strictly individually rational action pair, or any strict protected Nash equilibrium, constitutes a pure steady state, to which the process converges from non-negligible sets of initial aspirations. Applications to games of coordination, cooperation, oligopoly, and electoral competition are discussed.

    Original languageEnglish (US)
    Article number3
    JournalB.E. Journal of Theoretical Economics
    Issue number1
    StatePublished - 2001


    • aspirations
    • bounded rationality
    • cooperation
    • coordination
    • reinforcement learning

    ASJC Scopus subject areas

    • Economics, Econometrics and Finance(all)


    Dive into the research topics of 'Reinforcement Learning in Repeated Interaction Games'. Together they form a unique fingerprint.

    Cite this