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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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 70 (2010)
Issue (Month): 2 (November)
Pages: 472-487

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Handle: RePEc:eee:gamebe:v:70:y:2010:i:2:p:472-487

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Bounded rationality Chain Store Paradox Finite automata Imperfect recall Limited foresight Reasoning by analogy;

References

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  1. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February.
  2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
  3. 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.
  4. Philippe Jeniel, 2001. "Analogy-Based Expectation Equilibrium," Economics Working Papers 0003, Institute for Advanced Study, School of Social Science.
  5. Philippe Jehiel & Dov Samet, 2010. "Learning To Play Games In Extensive Form By Valuation," Levine's Working Paper Archive 391749000000000034, David K. Levine.
  6. Samuelson, Larry, 2001. "Analogies, Adaptation, and Anomalies," Journal of Economic Theory, Elsevier, vol. 97(2), pages 320-366, April.
  7. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  8. 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.
  9. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, 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. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  12. 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.
  13. Banks, J.S. & Sundaram, R.K., 1989. "Repeated Games, Finite Automata, And Complexity," RCER Working Papers 183, University of Rochester - Center for Economic Research (RCER).
  14. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-81, November.
  15. Rubinstein, Ariel, 1995. "On the Interpretation of Decision Problems with Imperfect Recall," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 324-324, December.
  16. Jehiel, Philippe, 2001. "Limited Foresight May Force Cooperation," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 369-91, April.
  17. 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.
  18. 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.
  19. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
  20. 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.
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