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COMMON REASONING IN GAMES: A LEWISIAN ANALYSIS OF COMMON KNOWLEDGE OF RATIONALITY

Published online by Cambridge University Press:  22 September 2014

Robin P. Cubitt  and
Robert Sugden
Robin P. Cubitt
Affiliation:
University of Nottingham, [email protected]
Robert Sugden
Affiliation:
University of East Anglia, [email protected]
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Abstract

We present a new class of models of players’ reasoning in non-cooperative games, inspired by David Lewis's account of common knowledge. We argue that the models in this class formalize common knowledge of rationality in a way that is distinctive, in virtue of modelling steps of reasoning; and attractive, in virtue of being able to represent coherently common knowledge of any consistent standard of individual decision-theoretic rationality. We contrast our approach with that of Robert Aumann (1987), arguing that the former avoids and diagnoses certain paradoxes to which the latter may give rise when extended in particular ways.

Type
Articles
Information
Economics & Philosophy , Volume 30 , Issue 3 , November 2014 , pp. 285 - 329
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Anderlini, L. 1990. Some notes on Church's thesis and the theory of games. Theory and Decision 29: 19–52.CrossRefGoogle Scholar
Asheim, G. B. and Dufwenberg, M.. 2003. Admissibility and common belief. Games and Economic Behavior 42: 208–234.CrossRefGoogle Scholar
Aumann, R. 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55: 1–18.CrossRefGoogle Scholar
Aumann, R. 1999 a. Interactive epistemology I: knowledge. International Journal of Game Theory 28: 263–300.CrossRefGoogle Scholar
Aumann, R. 1999 b. Interactive epistemology II: probability. International Journal of Game Theory 28: 301–314.CrossRefGoogle Scholar
Bacharach, M. O. L. 1987. A theory of rational decision in games. Erkenntnis 27: 17–55.CrossRefGoogle Scholar
Binmore, K. 1987. Modeling rational players: Part I. Economics and Philosophy 3: 179–214.CrossRefGoogle Scholar
Binmore, K. 1988. Modeling rational players: Part II. Economics and Philosophy 4: 9–55.CrossRefGoogle Scholar
Bonanno, G. 2012. Epistemic foundations of game theory. University of California, Davis, Department of Economics working paper 12–11.Google Scholar
Börgers, T. and Samuelson, L.. 1992. “Cautious” utility maximisation and iterated weak dominance. International Journal of Game Theory 21: 13–25.CrossRefGoogle Scholar
Brandenburger, A. 2007. The power of paradox: some recent developments in interactive epistemology. International Journal of Game Theory 35: 465–492.CrossRefGoogle Scholar
Brandenburger, A., Friedenberg, A. and Keisler, H. J.. 2008. Admissibility in games. Econometrica 76: 307–352.CrossRefGoogle Scholar
Cubitt, R. P. and Sugden, R.. 1994. Rationally justifiable play and the theory of noncooperative games. Economic Journal 104: 798–803.CrossRefGoogle Scholar
Cubitt, R. P. and Sugden, R.. 1997. Rationally justifiable play and the theory of noncooperative games. In Epistemic Logic and the Theory of Games and Decisions, ed. Bacharach, M. O. L., Gérard-Varet, L.-A., Mongin, P. and Shin, H. S., 293–302. Dordrecht: Kluwer.CrossRefGoogle Scholar
Cubitt, R. P. and Sugden, R.. 2003. Common knowledge, salience and convention: a reconstruction of David Lewis's game theory. Economics and Philosophy 19: 175–210.CrossRefGoogle Scholar
Cubitt, R. P. and Sugden, R.. 2011. The reasoning-based expected utility procedure. Games and Economic Behavior 71: 328–338.CrossRefGoogle Scholar
Gintis, H. 2009. The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences. Princeton, NJ: Princeton University Press.Google Scholar
Lewis, D. 1969. Convention: A Philosophical Study. Cambridge, MA: Harvard University Press.Google Scholar
Monderer, D. and Samet, D.. 1989. Approximating common knowledge with common beliefs. Games and Economic Behavior 1: 170–190.CrossRefGoogle Scholar
Nash, J. F. 1951. Non-cooperative games. Annals of Mathematics 54: 286–295.CrossRefGoogle Scholar
Norde, H. 1999. Bimatrix games have quasi-strict equilibria. Mathematical Programming 85: 35–49.CrossRefGoogle Scholar
Paternotte, C. 2011. Being realistic about common knowledge: a Lewisian approach. Synthese 183: 249–276.CrossRefGoogle Scholar
Pearce, D. G. 1984. Rationalizable strategic behavior and the problem of perfection. Econometrica 52: 1029–1050.CrossRefGoogle Scholar
Perea, A. 2011. An algorithm for proper rationalizability. Games and Economic Behavior 72: 510–525.CrossRefGoogle Scholar
Perea, A. 2012. Epistemic Game Theory: Reasoning and Choice. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Samuelson, L. 1992. Dominated strategies and common knowledge. Games and Economic Behavior 4: 284–313.CrossRefGoogle Scholar
Sillari, G. 2005. A logical framework for convention. Synthese 147: 379–400.CrossRefGoogle Scholar
Squires, D. 1998. Impossibility theorems for normal form games. Theory and Decision 44: 67–81.CrossRefGoogle Scholar
Vanderschraaf, P. 1998. Knowledge, equilibrium and convention. Erkenntnis 42: 65–87.CrossRefGoogle Scholar