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

  • Robin Cubitt

    ()

    (School of Economics, University of Nottingham)

  • Robert Sugden

    ()

    (School of Economics, University of East Anglia)

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.

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Paper provided by The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham in its series Discussion Papers with number 2011-01.

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Date of creation: Jan 2011
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Handle: RePEc:cdx:dpaper:2011-01
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  1. Robin P. Cubitt & Robert Sugden, 2009. "The reasoning-based expected utility procedure," Discussion Papers 2009-16, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  2. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
  3. Asheim,G.B. & Dufwenberg,M., 2000. "Admissibility and common belief," Memorandum 07/2000, Oslo University, Department of Economics.
  4. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
  5. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
  6. Cubitt, Robin P. & Sugden, Robert, 2003. "Common Knowledge, Salience And Convention: A Reconstruction Of David Lewis' Game Theory," Economics and Philosophy, Cambridge University Press, vol. 19(02), pages 175-210, October.
  7. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
  8. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer, vol. 35(4), pages 465-492, April.
  9. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(01), pages 9-55, April.
  10. 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, June.
  11. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
  12. Cubitt, Robin P & Sugden, Robert, 1994. "Rationally Justifiable Play and the Theory of Non-cooperative Games," Economic Journal, Royal Economic Society, vol. 104(425), pages 798-803, July.
  13. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
  14. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
  15. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  16. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
  17. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
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