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Learning Equilibria in Games Played by Heterogeneous Populations


  • Y.M. Kaniovski
  • A.V. Kryazhimskii
  • H.P. Young


Consider two populations of agents who learn to play a game through. repetition. In fictitious play, each agent chooses a best replay to the frequency distribution of actions taken by the other side. A natural variant of this model is to assume that agents are heterogeneous in their information and their behavioral response rules. Assume that each agent knows only a randomly drawn sample of past actions. Given their information, agents sometimes choose best replies, and sometimes they imitate behavior in their own population. In contrast to the stochastic best reply dynamics studied by Fudenberg and Kreps (1993), Kaniovski and Young (1995), and Benaiem and Hirsch (1994), such process can cycle in a 2x2 game even when the probability of imitators is arbitrarily small. We show how to characterize its asymptotic behavior through an extension of Bendixon's theory for excluding cycles combined with standard techniques from stochastic approximation. \f2Journal of Economic Literature\f1 Classification Numbers: C44, C73, D83.

Suggested Citation

  • Y.M. Kaniovski & A.V. Kryazhimskii & H.P. Young, 1997. "Learning Equilibria in Games Played by Heterogeneous Populations," Working Papers ir97017, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:ir97017

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    References listed on IDEAS

    1. Casar, José I., 1995. "La industria mexicana a principios de los noventa," Sede de la CEPAL en Santiago (Estudios e Investigaciones) 30345, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    2. Cimoli, Mario & Dosi, Giovanni, 1995. "Technological Paradigms, Patterns of Learning and Development: An Introductory Roadmap," Journal of Evolutionary Economics, Springer, vol. 5(3), pages 243-268, September.
    3. Mortimore, Michael, 1995. "Restructuring and international competitiveness: the Mexican automobile industry," Sede de la CEPAL en Santiago (Estudios e Investigaciones) 30470, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    4. Calderón Hoffmann, Alvaro & Mortimore, Michael & Peres Núñez, Wilson, 1995. "Mexico's incorporation into the new industrial order: foreign investment as a source of international competitiveness," Desarrollo Productivo 21, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
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    Cited by:

    1. A.F. Kleimenov & A.V. Kryazhimskii, 1998. "Normal Behavior, Altruism and Aggression in Cooperative Game Dynamics," Working Papers ir98076, International Institute for Applied Systems Analysis.

    More about this item

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness


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