An Epistemic Course in Game Theory List of references: 1. Introduction • Adam Brandenburger (2007): “The power of paradox: Some recent results in interactive epistemology”, International Journal of Game Theory 35, 465-492. • Geir Asheim (2006): “The consistent preferences approach to deductive reasoning in games”, Theory and Decision Library, Springer, Dordrecht, The Netherlands. • Andrés Perea: “Reasoning about your opponents: An epistemic course in game theory”, In progress. 2. Common belief in rationality • Tommy Chin-Chiu Tan and Sérgio Ribeiro da Costa Werlang (1988): “The Bayesian foundations of solution concepts of games”, Journal of Economic Theory 45, 370-391. • Kaushik Basu (1994): “The traveler’s dilemma: Paradoxes of rationality in game theory”, American Economic Review 36, 391-396. • Douglas Bernheim (1984): “Rationalizable strategic behavior”, Econometrica 52, 1007-1028. • David Pearce (1984): “Rationalizable strategic behavior and the problem of perfection”, Econometrica 52, 1029-1050. • Adam Brandenburger and Amanda Friedenberg (2006): “Intrinsic correlation in games”, Downloadable from http://pages.stern.nyu.edu/~abranden/

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3. Self-referential reasoning • John Nash (1951): “Non-cooperative games”, Annals of Mathematics 54, 286-295. • Andrés Perea (2007): “Nash equilibrium as an expression of selfreferential reasoning”, Downloadable from http://www.personeel.unimaas.nl/a.perea/WorkingPapers.htm • Adam Brandenburger and Eddie Dekel (1987): “Rationalizability and correlated equilibria”, Econometrica 55, 1391-1402. • Robert Aumann and Adam Brandenburger (1995): “Epistemic conditions for Nash equilibrium”, Econometrica 63, 1161-1180. • Geir Asheim (2006): “The consistent preferences approach to deductive reasoning in games”, Theory and Decision Library, Springer, Dordrecht, The Netherlands. 4. Cautious reasoning • Adam Brandenburger (1992): “Lexicographic probabilities and iterated admissibility”, in Economic Analysis of Markets and Games, Editors: Partha Dasgupta, Douglas Gale, Oliver Hart and Eric Maskin, The MIT Press, Cambridge, MA. • Tilman Börgers (1994): “Weak dominance and approximate common knowledge”, Journal of Economic Theory 64, 265-276. • Eddie Dekel and Drew Fudenberg (1990): “Rational behavior with payoff uncertainty”, Journal of Economic Theory 52, 243-267. • Reinhard Selten (1975): “Reexamination of the perfectness concept for equilibrium points in extensive games”, International Journal of Game Theory 4, 25-55. • Adam Brandenburger, Amanda Friedenberg and H. Jerome Keisler (2006): “Admissibility in games”, Downloadable from http://pages.stern.nyu.edu/~abranden/ • Geir Asheim (2001): “Proper rationalizability in lexicographic beliefs”, International Journal of Game Theory 30, 453-478. 2

• Frank Schuhmacher (1999): “Proper rationalizability and backward induction”, International Journal of Game Theory 28, 599-615. 5. Belief revision in dynamic games • Elchanan Ben-Porath (1997): “Rationality, Nash equilibrium and backwards induction in perfect-information games”, Review of Economic Studies 64, 23-46. • Philip Reny (1992a): “Backward induction, normal form perfection and explicable equilibria”, Econometrica 60, 627-649. • Philip Reny (1992b): “Rationality in extensive-form games”, Journal of Economic Perspectives 6, 103-118. • Philip Reny (1993): “Common belief and the theory of games with perfect information”, Journal of Economic Theory 59, 257-274. 6. Belief in the opponents’ future rationality • Ernst Zermelo (1913): “Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels”, Proceedings Fifth International Congress of Mathematicians 2, 501-504. • Geir Asheim (2002): “On the epistemic foundation for backward induction”, Mathematical Social Sciences 44, 121-144. • Robert Aumann (1995): “Backward induction and common knowledge of rationality”, Games and Economic Behavior 8, 6-19. • Dov Samet (1996): “Hypothetical knowledge and games with perfect information”, Games and Economic Behavior 17, 230-251. • Dieter Balkenborg and Eyal Winter (1997): “A necessary and sufficient epistemic condition for playing backward induction”, Journal of Mathematical Economics 27, 325-345. • Robert Stalnaker (1998): “Belief revision in games: forward and backward induction”, Mathematical Social Sciences 36, 31-56. • Antonio Quesada (2002): “Belief system foundations of backward induction”, Theory and Decision 53, 393-403. 3

• Antonio Quesada (2003): “From common knowledge of rationality to backward induction”, International Game Theory Review 5, 127-137. • Thorsten Clausing (2003): “Doxastic conditions for backward induction”, Theory and Decision 54, 315-336. • Yossi Feinberg (2005): “Subjective reasoning - dynamic games”, Games and Economic Behavior 52, 54-93. • Geir Asheim and Andrés Perea (2005): “Sequential and quasi-perfect rationalizability in extensive games”, Games and Economic Behavior 53, 15-42. • Andrés Perea (2007a): “Minimal belief revision leads to backward induction”, Downloadable from http://www.personeel.unimaas.nl/a.perea/WorkingPapers.htm • Andrés Perea (2007b): “Epistemic foundations for backward induction: An overview”, Forthcoming in proceedings volume entitled "Interactive Logic", to be published as volume 1 of the new book series "Texts in Logic and Games" by Amsterdam University Press (AUP). Downloadable from http://www.personeel.unimaas.nl/a.perea/WorkingPapers.htm 7. Strong belief in the opponents’ rationality • Pierpaolo Battigalli and Marciano Siniscalchi (2002): “Strong belief and forward induction reasoning”, Journal of Economic Theory 106, 356-391. • David Pearce (1984): “Rationalizable strategic behavior and the problem of perfection”, Econometrica 52, 1029-1050. • Pierpaolo Battigalli (1997): “On rationalizability in extensive games”, Journal of Economic Theory 74, 40-61. • Andrés Perea (2006a): “Proper belief revision and rationalizability in dynamic games”, International Journal of Game Theory 34, 529-559. • Makoto Shimoji and joel Watson (1998): “Conditional dominance, rationalizability, and game forms”, Journal of Economic Theory 83, 161-195. 4

• Elchanan Ben-Porath and Eddie Dekel (1992): “Signaling future actions and the potential for sacrifice”, Journal of Economic Theory 57, 36-51. • Makoto Shimoji (2002): “On forward induction in money-burning games”, Economic Theory 19, 637-648. • Eric van Damme (1989): “Stable equilibria and forward induction”, Journal of Economic Theory 48, 476-496. • Perea, A. (2006b), “Proper belief revision and equilibrium in dynamic games”, Forthcoming in Journal of Economic Theory. Downloadable from http://www.personeel.unimaas.nl/a.perea/WorkingPapers.htm

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