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Interaction dynamics of two reinforcement learners

  • Walter Gutjahr

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    The paper investigates a stochastic model where two agents (persons, companies, institutions, states, software agents or other) learn interactive behavior in a series of alternating moves. Each agent is assumed to perform “stimulus-response-consequence” learning, as studied in psychology. In the presented model, the response of one agent to the other agent's move is both the stimulus for the other agent's next move and part of the consequence for the other agent's previous move. After deriving general properties of the model, especially concerning convergence to limit cycles, we concentrate on an asymptotic case where the learning rate tends to zero (“slow learning”). In this case, the dynamics can be described by a system of deterministic differential equations. For reward structures derived from [2×2] bimatrix games, fixed points are determined, and for the special case of the prisoner's dilemma, the dynamics is analyzed in more detail on the assumptions that both agents start with the same or with different reaction probabilities. Copyright Springer-Verlag 2006

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    File URL: http://hdl.handle.net/10.1007/s10100-006-0160-y
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    Article provided by Springer & Slovak Society for Operations Research & Hungarian Operational Research Society & Czech Society for Operations Research & Österr. Gesellschaft für Operations Research (ÖGOR) & Slovenian Society Informatika - Section for Operational Research & Croatian Operational Research Society in its journal Central European Journal of Operations Research.

    Volume (Year): 14 (2006)
    Issue (Month): 1 (February)
    Pages: 59-86

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    Handle: RePEc:spr:cejnor:v:14:y:2006:i:1:p:59-86
    DOI: 10.1007/s10100-006-0160-y
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    1. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    2. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
    3. J.-F. Laslier & R. Topol & B. Walliser, 1999. "A behavioral learning process in games," THEMA Working Papers 99-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    4. Richard J. Herrnstein & Drazen Prelec, 1991. "Melioration: A Theory of Distributed Choice," Journal of Economic Perspectives, American Economic Association, vol. 5(3), pages 137-156, Summer.
    5. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    6. Benaim, Michel & Weibull, Jörgen W., 2000. "Deterministic Approximation of Stochastic Evolution in Games," Working Paper Series 534, Research Institute of Industrial Economics, revised 30 Oct 2001.
    7. Brian Skyrms & Robin Pemantle, 2004. "Learning to Network," Levine's Bibliography 122247000000000436, UCLA Department of Economics.
    8. Greenwald, Amy & Friedman, Eric J. & Shenker, Scott, 2001. "Learning in Network Contexts: Experimental Results from Simulations," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 80-123, April.
    9. John G. Cross, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 87(2), pages 239-266.
    10. M. Posch & A. Pichler & K. Sigmund, 1998. "The Efficiency of Adapting Aspiration Levels," Working Papers ir98103, International Institute for Applied Systems Analysis.
    11. Ron Smith & Martin Sola & Fabio Spagnolo, 2000. "The Prisoner's Dilemma and Regime-Switching in the Greek-Turkish Arms Race," Journal of Peace Research, Peace Research Institute Oslo, vol. 37(6), pages 737-750, November.
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