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Modelling equilibrium play as governed by analogy and limited foresight

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  • Wichardt, Philipp C.

Abstract

This paper proposes a bounded rationality approach to model equilibrium play in games. It is based on the observation that decision makers often do not seem to fully distinguish between different but seemingly similar decisions and tend to treat such similar decisions in a standardised/habitual way. To capture this, each player's information partition is derived from a similarity grouping of decisions based on the local structure of the game - equality of available actions and analogy of locally foreseen subtrees - and possibly refined by additional information about crucial aspects of past play. The equilibrium concept considered is a (trembling-hand) perfect Nash equilibrium (Selten, 1975), in which players are required to choose the same (routine) behaviour for similar decisions. Based on the approach, it is shown how the Chain Store Paradox (Selten, 1978) can be resolved, and how mixed equilibria in the Centipede Game (Rosenthal, 1981) can be rationalised.

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  • Wichardt, Philipp C., 2010. "Modelling equilibrium play as governed by analogy and limited foresight," Games and Economic Behavior, Elsevier, vol. 70(2), pages 472-487, November.
    • Handle: RePEc:eee:gamebe:v:70:y:2010:i:2:p:472-487
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    References listed on IDEAS

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    1. Jehiel, Philippe & Samet, Dov, 2005. "Learning to play games in extensive form by valuation," Journal of Economic Theory, Elsevier, vol. 124(2), pages 129-148, October.
    2. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    3. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July.
    4. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    5. Piccione, Michele & Rubinstein, Ariel, 1997. "The Absent-Minded Driver's Paradox: Synthesis and Responses," Games and Economic Behavior, Elsevier, vol. 20(1), pages 121-130, July.
    6. Philippe Jehiel, 2001. "Limited Foresight May Force Cooperation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 369-391.
    7. Binmore, Ken & McCarthy, John & Ponti, Giovanni & Samuelson, Larry & Shaked, Avner, 2002. "A Backward Induction Experiment," Journal of Economic Theory, Elsevier, vol. 104(1), pages 48-88, May.
    8. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    9. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    10. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    11. Jude Kline, J., 2002. "Minimum Memory for Equivalence between Ex Ante Optimality and Time-Consistency," Games and Economic Behavior, Elsevier, vol. 38(2), pages 278-305, February.
    12. Abraham Neyman, 1998. "Finitely Repeated Games with Finite Automata," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 513-552, August.
    13. Banks, Jeffrey S. & Sundaram, Rangarajan K., 1990. "Repeated games, finite automata, and complexity," Games and Economic Behavior, Elsevier, vol. 2(2), pages 97-117, June.
    14. Samuelson, Larry, 2001. "Analogies, Adaptation, and Anomalies," Journal of Economic Theory, Elsevier, vol. 97(2), pages 320-366, April.
    15. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    16. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    17. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
    18. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February.
    19. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    20. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    21. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
    22. Wichardt, Philipp C., 2008. "Existence of Nash equilibria in finite extensive form games with imperfect recall: A counterexample," Games and Economic Behavior, Elsevier, vol. 63(1), pages 366-369, May.
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