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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. Philippe Jehiel & Dov Samet, 2010. "Learning to play games in extensive form by valuation," Levine's Working Paper Archive 391749000000000040, David K. Levine.
  2. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  3. 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.
  4. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  5. Jehiel, Philippe, 2001. "Limited Foresight May Force Cooperation," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 369-91, April.
  6. Philippe Jehiel, 2005. "Analogy-Based Expectation Equilibrium," Levine's Bibliography 784828000000000106, UCLA Department of Economics.
  7. Rubinstein, Ariel, 1995. "On the Interpretation of Decision Problems with Imperfect Recall," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 324-324, December.
  8. David Kreps & Paul Milgrom & John Roberts & Bob Wilson, 2010. "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Levine's Working Paper Archive 239, David K. Levine.
  9. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  10. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  11. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
  12. 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.
  13. 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.
  14. 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.
  15. Binmore,K. & McCarthy,J. & Ponti,G. & ..., 1999. "A backward induction experiment," Working papers 34, Wisconsin Madison - Social Systems.
  16. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
  17. Samuelson, Larry, 2001. "Analogies, Adaptation, and Anomalies," Journal of Economic Theory, Elsevier, vol. 97(2), pages 320-366, April.
  18. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February.
  19. 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.
  20. 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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