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

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  • Robin P. 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.

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Paper provided by School of Economics, University of East Anglia, Norwich, UK. in its series Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) with number 11-05.

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Date of creation: 01 Feb 2011
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Handle: RePEc:uea:wcbess:11-05

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

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  1. Robin P. Cubitt & Robert Sugden, 2009. "The reasoning-based expected utility procedure," Discussion Papers, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham 2009-16, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  2. 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, December.
  3. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, Econometric Society, vol. 66(4), pages 929-938, July.
  4. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, Springer, vol. 28(3), pages 301-314.
  5. 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.
  6. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, Springer, vol. 28(3), pages 263-300.
  7. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 1-18, January.
  8. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, Econometric Society, vol. 66(4), pages 923-928, July.
  9. Asheim,G.B. & Dufwenberg,M., 2000. "Admissibility and common belief," Memorandum, Oslo University, Department of Economics 07/2000, Oslo University, Department of Economics.
  10. Cubitt, Robin P & Sugden, Robert, 1994. "Rationally Justifiable Play and the Theory of Non-cooperative Games," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 104(425), pages 798-803, July.
  11. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  12. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer, Springer, vol. 35(4), pages 465-492, April.
  13. 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.
  14. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
  15. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(01), pages 9-55, April.
  16. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  17. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, Springer, vol. 21(1), pages 13-25.
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