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Interpreting Knowledge in the Backward Induction Problem1

Published online by Cambridge University Press:  03 January 2012

Ken Binmore
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Abstract

Robert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

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Type
Research Article
Information
Episteme , Volume 8 , Issue 3 , October 2011 , pp. 248 - 261
Copyright
Copyright © Cambridge University Press 2011

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References

Aumann, R. 1995. “Backward Induction and Common Knowledge of Rationality.” Games and Economic Behavior 8: 6–19.Google Scholar
Aumann, R. 1996a. “Reply to Binmore.” Games and Economic Behavior 17: 138–46.Google Scholar
Aumann, R. 1996b. “Reply to Binmore and Samuelson.” In Arrow, K. J. et al. (eds.), The Rational Foundations of Economic Behavior, pp. 130–1. London and Basingstoke: Macmillan.Google Scholar
Aumann, R. 1998. “On the Centipede Game.” Games and Economic Behavior 23: 97–105.Google Scholar
Bicchieri, C. 1988. “Common Knowledge and Backwards Induction: A Solution to the Paradox.” In Vardi, M. (ed.), Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 381–93. Los Altos, CA: Morgan Kaufmann.Google Scholar
Binmore, K. 1987. “Modeling Rational Players II.” Economics and Philosophy 4: 179–214.Google Scholar
Binmore, K. 1996. “A Note on Backward Induction.” Games and Economic Behavior 17: 135–7.Google Scholar
Binmore, K. 1997. “Rationality and Backward Induction.” Journal of Economic Methodology 4: 23–41.Google Scholar
Binmore, K. 2007. Playing for Real. New York: Oxford University Press.Google Scholar
Binmore, K. 2008. “Do Conventions Need to Be Common Knowledge?” Topoi 27: 17–27.Google Scholar
Binmore, K. 2009. Rational Decisions. Princeton: Princeton University Press.Google Scholar
Fudenberg, D, Kreps, D., and Levine, D.. 1988. “On the Robustness of Equilibrium Refinements.” Journal of Economic Theory 44: 354–80.Google Scholar
Halpern, J. 2001. “Substantive Reasoning and Backward Induction.” Games and Economic Behavior 37: 425–35.Google Scholar
Kolmogorov, A. 1950. Foundations of the Theory of Probability. New York: Chelsea.Google Scholar
Kreps, D, Milgrom, P., Roberts, J., and Wilson, R.. 1982. “Rational Cooperation in the Finitely Repeated Prisoners' Dilemma.” Journal of Economic Theory 27: 245–52.Google Scholar
Kuhn, T. 1962. The Structure of Scientific Revolutions. Chicago: University of Chicago Press.Google Scholar
Lewis, D. 1973. Counterfactuals. Oxford: Blackwell.Google Scholar
Myerson, R. 1991. Game Theory: Analysis of Conflict. Cambridge, MA: Harvard University Press.Google Scholar
Reny, P. 1992. “Rationality in Extensive Form Games.” Journal of Economic Perspectives 6: 103–18.Google Scholar
Russell, B. 1917/2007. Mysticism and Logic. Nottingham: Spokesman.Google Scholar
Samet, D. 1996. “Hypothetical Knowledge and Games with Perfect Information.” Games and Economic Behavior 17: 230–51.Google Scholar
Savage, L. 1954. The Foundations of Statistics. New York: Wiley.Google Scholar
Selten, R. 1975. “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive-Games.” International Journal of Game Theory 4: 25–55.Google Scholar
Selten, R. 1978. “The Chain-Store Paradox.” Theory and Decision 9: 127–59.Google Scholar
Selten, R and Leopold, U.. 1982. “Subjunctive Conditionals in Decision Theory and Game Theory.” In Stegmüller, W., Balzer, W., and Spohn, W. (eds.), Philosophy of Economics: Proceedings, Munich, July 1981. Berlin: Springer-Verlag.Google Scholar
Sobel, J. 1994. Taking Chances. Cambridge: Cambridge University Press.Google Scholar
Stalnaker, R. 1996. “Knowledge, Belief and Counterfactual Reasoning in Games.” Economics and Philosophy 12: 133–63.Google Scholar
Wittgenstein, L. 1969. On Certainty. Anscombe, G. and von Wright, G. (eds.). Paul, D. and Anscombe, G. (trans.). Oxford: Basil Blackwell.Google Scholar