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Common reasoning in games: a Lewisian analysis of common knowledge of rationality

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  • Robin Cubitt

    () (School of Economics, University of Nottingham)

  • Robert Sugden

    () (School of Economics, University of East Anglia)

Abstract

The game-theoretic assumption of ‘common knowledge of rationality’ leads to paradoxes when rationality is represented in a Bayesian framework as cautious expected utility maximisation with independent beliefs (ICEU). We diagnose and resolve these paradoxes by presenting a new class of formal models of players’ reasoning, inspired by David Lewis’s account of common knowledge, in which the analogue of common knowledge is derivability in common reason. We show that such models can consistently incorporate any of a wide range of standards of decision-theoretic practical rationality. We investigate the implications arising when the standard of decision-theoretic rationality so assumed is ICEU.

Suggested Citation

  • Robin Cubitt & Robert Sugden, 2011. "Common reasoning in games: a Lewisian analysis of common knowledge of rationality," Discussion Papers 2011-01, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  • Handle: RePEc:not:notcdx:2011-01
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
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    1. repec:jdm:journl:v:13:y:2018:i:1:p:137-149 is not listed on IDEAS

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    Keywords

    Common reasoning; common knowledge; common knowledge of rationality; David Lewis; Bayesian models of games;

    JEL classification:

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

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