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Rationalizable partition-confirmed equilibrium with heterogeneous beliefs

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  • Fudenberg, Drew
  • Kamada, Yuichiro

Abstract

Many models of learning in games implicitly or explicitly assume there are many agents in the role of each player. In principle this allows different agents in the same player role to have different beliefs and play differently, and this is known to occur in laboratory experiments. To explore the impact of this heterogeneity, along with the idea that subjects use their information about other players' payoffs, we define rationalizable partition-confirmed equilibrium (RPCE). We provide several examples to highlight the impact of heterogeneous beliefs, and show how mixed strategies can correspond to heterogeneous play in a large population. We also show that every heterogeneous-belief RPCE can be approximated by a RPCE in a model where every agent in a large pool is a separate player.

Suggested Citation

  • Fudenberg, Drew & Kamada, Yuichiro, 2018. "Rationalizable partition-confirmed equilibrium with heterogeneous beliefs," Games and Economic Behavior, Elsevier, vol. 109(C), pages 364-381.
    • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:364-381
    DOI: 10.1016/j.geb.2017.12.021
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    References listed on IDEAS

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    1. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February.
    4. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 1999. "Payoff Information and Self-Confirming Equilibrium," Journal of Economic Theory, Elsevier, vol. 89(2), pages 165-185, December.
    5. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-573, May.
    6. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    7. Fudenberg, Drew & Kreps, David M., 1995. "Learning in extensive-form games I. Self-confirming equilibria," Games and Economic Behavior, Elsevier, vol. 8(1), pages 20-55.
    8. Drew Fudenberg & David K. Levine, 1997. "Measuring Players' Losses in Experimental Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 507-536.
    9. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    10. Vesna Prasnikar & Alvin E. Roth, 1992. "Considerations of Fairness and Strategy: Experimental Data from Sequential Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 865-888.
    11. , & ,, 2015. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, vol. 10(3), September.
    12. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November.
    13. ,, 2013. "Rationalizable conjectural equilibrium: A framework for robust predictions," Theoretical Economics, Econometric Society, vol. 8(2), May.
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    Cited by:

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    2. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    3. Battigalli, P. & Catonini, E. & Lanzani, G. & Marinacci, M., 2019. "Ambiguity attitudes and self-confirming equilibrium in sequential games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 1-29.
    4. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Schmeidler, David, 2022. "Equilibria of nonatomic anonymous games," Games and Economic Behavior, Elsevier, vol. 135(C), pages 110-131.
    5. Fudenberg, Drew & He, Kevin, 2020. "Payoff information and learning in signaling games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 96-120.
    6. Clark, Daniel & Fudenberg, Drew & He, Kevin, 2022. "Observability, dominance, and induction in learning models," Journal of Economic Theory, Elsevier, vol. 206(C).

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    More about this item

    Keywords

    Rationalizability; Extensive-form games; Self-confirming equilibrium; Heterogeneous beliefs; Purification; Random matching;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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