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Overt and Underlying Games: The Case of the Centipede

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  • Carlo Beretta

Abstract

Making use of and following substantive rationality is a costly and not always feasible option. In games, this option generates two levels of reasoning. The player has to decide how to play the overt game, but this requires him to decide how to play an underlying game in which the alternatives are to follow either substantive rationality or a different rule, here that of reasonableness, in playing the overt game. A strategy is reasonable if coupled with its best response it results in the player that adopts it achieving the highest payoff among those dominating the Nash equilibria of the overt game. The underlying game can have more than one equilibrium. Substantive rationality in the underlying game can justify behaviour which is at odds with substantively rational behaviour in the overt game. The case of the centipede is used as an example

Suggested Citation

  • Carlo Beretta, 2010. "Overt and Underlying Games: The Case of the Centipede," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 118(1), pages 27-45.
  • Handle: RePEc:vep:journl:y:2010:v:118:i:1:p:27-45
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    Keywords

    Common knowledge; Rationality; Backward induction; Reasonableness; Incomplete information; Centipede game;

    JEL classification:

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

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