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Reinforcement Learning in Repeated Interaction Games

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Author Info

  • Bendor Jonathan

    ()
    (Stanford University)

  • Mookherjee Dilip

    ()
    (Boston University)

  • Ray Debraj

    ()
    (New York University)

Abstract

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.

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Bibliographic Info

Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

Volume (Year): 1 (2001)
Issue (Month): 1 (March)
Pages: 1-44

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Handle: RePEc:bpj:bejtec:v:advances.1:y:2001:i:1:n:3

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Cited by:
  1. Dziubiński, Marcin & Roy, Jaideep, 2012. "Popularity of reinforcement-based and belief-based learning models: An evolutionary approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 433-454.
  2. Martorana, Marco & Mazza, Isidoro, 2010. "Satisfaction and adaptation in voting behavior: an empirical exploration," DEMQ Working Paper Series 2010/6, University of Catania, Department of Economics and Quantitative Methods.
  3. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
  4. Duffy, John, 2006. "Agent-Based Models and Human Subject Experiments," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 19, pages 949-1011 Elsevier.
  5. Marcin Dziubinski & Jaideep Roy, 2007. "Endogenous Selection of Aspiring and Rational rules in Coordination Games," CEDI Discussion Paper Series 07-14, Centre for Economic Development and Institutions(CEDI), Brunel University.
  6. Siegfried Berninghaus & Werner G?th & M. Vittoria Levati & Jianying Qiu, 2009. "Satisficing in sales competition: experimental evidence," Working Papers 2009-14, Faculty of Economics and Statistics, University of Innsbruck.
  7. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.

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