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Common reasoning in games

  • Robin P. Cubitt


    (School of Economics, University of Nottingham)

  • Robert Sugden


    (School of Economics, University of East Anglia)

This paper makes three related contributions to noncooperative game theory: (i) a solution concept (the “ICEU solution”), which is generated by an iterative procedure that constructs trinary partitions of strategy sets and deals with problems arising from weak dominance; (ii) a class of models of players’ reasoning, inspired by David Lewis’s work on common knowledge, which can together represent common knowledge of rationality for any consistent conception of individual practical rationality; and, using these ingredients, (iii) a diagnosis of paradoxes associated with the concept of common knowledge of rationality, as represented in Bayesian models of games.

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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 2008-01.

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Date of creation: Mar 2008
Date of revision:
Handle: RePEc:cdx:dpaper:2008-01
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  1. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  2. Asheim, Geir B. & Dufwenberg, Martin, 2000. "Amissibility and Common Belief," Research Papers in Economics 2000:6, Stockholm University, Department of Economics.
  3. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(01), pages 9-55, April.
  4. 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.
  5. 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.
  6. Mandler, Michael, 2007. "Strategies as states," Journal of Economic Theory, Elsevier, vol. 135(1), pages 105-130, July.
  7. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
  8. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
  9. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
  10. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
  11. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
  12. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
  13. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  14. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
  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. Werlang, Sérgio Ribeiro da Costa & Chin-Chiu Tan, Tommy, 1987. "The Bayesian Foundations of Solution Concepts of Games," Economics Working Papers (Ensaios Economicos da EPGE) 111, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  17. 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.
  18. 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.
  19. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  20. Larry Samuelson, 2004. "Modeling Knowledge in Economic Analysis," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 367-403, June.
  21. Martin Dufwenberg & Mark Stegeman, 2002. "Existence and Uniqueness of Maximal Reductions Under Iterated Strict Dominance," Econometrica, Econometric Society, vol. 70(5), pages 2007-2023, September.
  22. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
  23. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
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