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Reinforcement Learning in Repeated Interaction Games

Author

Listed:
  • 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.

Suggested Citation

  • Bendor Jonathan & Mookherjee Dilip & Ray Debraj, 2001. "Reinforcement Learning in Repeated Interaction Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, March.
  • Handle: RePEc:bpj:bejtec:v:advances.1:y:2001:i:1:n:3
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    Citations

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    Cited by:

    1. 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.
    2. Jeffrey Carpenter & Peter Matthews, 2005. "No Switchbacks: Rethinking Aspiration-Based Dynamics in the Ultimatum Game," Theory and Decision, Springer, pages 351-385.
    3. Heymann, D. & Kawamura, E. & Perazzo, R. & Zimmermann, M.G., 2014. "Behavioral heuristics and market patterns in a Bertrand–Edgeworth game," Journal of Economic Behavior & Organization, Elsevier, vol. 105(C), pages 124-139.
    4. Guney, Begum & Richter, Michael, 2015. "An experiment on aspiration-based choice," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 512-526.
    5. Martorana, Marco F. & Mazza, Isidoro, 2012. "Adaptive voting: an empirical analysis of participation and choice," MPRA Paper 36165, University Library of Munich, Germany.
    6. Napel, Stefan, 2003. "Aspiration adaptation in the ultimatum minigame," Games and Economic Behavior, Elsevier, vol. 43(1), pages 86-106, April.
    7. Jeffrey Carpenter & Peter Matthews, 2005. "No Switchbacks: Rethinking Aspiration-Based Dynamics in the Ultimatum Game," Theory and Decision, Springer, pages 351-385.
    8. 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.
    9. MacLeod, W. Bentley & Pingle, Mark, 2005. "Aspiration uncertainty: its impact on decision performance and process," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 617-629, April.
    10. Peiran Jiao & Heinrich H. Nax, 2016. "When is Market the Benchmark? Reinforcement Evidence from Repurchase Decisions," Economics Series Working Papers 781, University of Oxford, Department of Economics.
    11. Akihiko Matsui & In-Koo Cho, 2008. "Matching, Repeated Game and Aspiration," 2008 Meeting Papers 75, Society for Economic Dynamics.
    12. Siegfried Berninghaus & Werner Güth & M. Vittoria Levati & Jianying Qiu, 2006. "Satisficing in sales competition: experimental evidence," Papers on Strategic Interaction 2006-32, Max Planck Institute of Economics, Strategic Interaction Group.
    13. Dziubinski, Marcin & Roy, Jaideep, 2007. "Endogenous selection of aspiring and rational rules in coordination games," MPRA Paper 5941, University Library of Munich, Germany.
    14. Heinrich, Torsten & Gräbner, Claudius, 2015. "Beyond Equilibrium: Revisiting Two-Sided Markets from an Agent-Based Modeling Perspective," MPRA Paper 67860, University Library of Munich, Germany.
    15. Segismundo S. Izquierdo & Luis R. Izquierdo & Nicholas M. Gotts, 2008. "Reinforcement Learning Dynamics in Social Dilemmas," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, pages 1-1.
    16. 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.
    17. Akihiko Matsui & In-Koo Cho, 2010. "Aspiration, Sympathy and Minmax Outcome," 2010 Meeting Papers 57, Society for Economic Dynamics.
    18. Cui Zhiwei & Zhai Jian & Liu Xuan, 2009. "The Efficiency of Observability and Mutual Linkage," The B.E. Journal of Theoretical Economics, De Gruyter, pages 1-36.
    19. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
    20. In-Koo Cho & Akihiko Matsui, 2012. "A Dynamic Foundation of the Rawlsian Maxmin Criterion," Dynamic Games and Applications, Springer, vol. 2(1), pages 51-70, March.
    21. Schuster, Stephan, 2012. "Applications in Agent-Based Computational Economics," MPRA Paper 47201, University Library of Munich, Germany.

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