Tang, Qianfeng (2010): Interim Partially Correlated Rationalizability.
Download (294Kb) | Preview
In game theory, there is a basic methodological dichotomy between Harsanyi's "game-theoretic" view and Aumann's "Bayesian decision-theoretic" view of the world. We follow the game-theoretic view, propose and study interim partially correlated rationalizability for games with incomplete information. We argue that the distinction between this solution concept and the interim correlated rationalizability studied by Dekel, Fudenberg and Morris (2007) is fundamental, in that the latter implicitly follows Aumann's Bayesian view.
Our main result shows that two types provide the same prediction in interim partially correlated rationalizability if and only if they have the same infinite hierarchy of beliefs over conditional beliefs. We also establish an equivalence result between this solution concept and the Bayesian solution--a notion of correlated equilibrium proposed by Forges (1993).
|Item Type:||MPRA Paper|
|Original Title:||Interim Partially Correlated Rationalizability|
|Keywords:||Games with incomplete information, Rationalizability, Common knowledge, Hierarchies of beliefs.|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||Qianfeng Tang|
|Date Deposited:||18. Nov 2010 10:22|
|Last Modified:||15. Feb 2013 21:07|
 Aliprantis, Charalambos D. and Kim C. Border (2006), "In�nite dimensional analysis: A Hitchhiker�s guide," third edition. Springer-Verlag, New York.
 Bernheim, Douglas (1984), "Rationalizable strategic behavior." Econometrica, 52, 1007-1028.
 Brandenburger, Adam and Amanda Friedenberg (2009), �Intrinsic correlation in games.�Journal of Economic Theory, 141, 28-67.
 Brandenburger, Adam and Eddie Dekel (1993), Rationalizability and correlated equilibria.�Econometrica, 55, 1391-1402.
 Brandenburger, Adam and Eddie Dekel (1993), �Hierarchies of beliefs and common knowledge.�Journal of Economic Theory, 59, 189-198.
 Dekel, Eddie, Drew Fudenberg and Stephen Morris (2007), �Interim correlated rationalizability.�Theoretical Economics, 2, 15-40.
 Dekel, Eddie, Drew Fudenberg and Stephen Morris (2006), �Topologies on types.�Theoretical Economics, 1, 275-309.
 Durrett, Richard (2004), "Probability: Theory and Examples," third edition. Duxbury Press.
 Ely, Jeff and Marcin Peski (2006), �Hierarchies of belief and interim rationalizability.� Theoretical Economics, 1, 19-65.
 Forges, Françoise (1993), �Five legitimate de�nitions of correlated equilibrium in games with incomplete information.�Theory and decision, 35, 277-310.
 Forges, Françoise (2006), �Correlated equilibrium in games with incomplete information revisited.�Theory and decision, 61, 329-344.
 Gossner, Olivier and Jean-François Mertens (2001), �The value of information in zero-sum games.�working paper.
 Harsanyi, John (1967-1968), "Games with incomplete information played by �Bayesian� players, Parts I, II, III." Management Science, 14, 159-182, 320-334, 486-502.
 Lehrer, Ehud, Dinah Rosenberg and Eran Shmaya (2006), �Signaling and mediation in Bayesian games.�working paper.
 Liu, Qingmin (2009), �On redundant types and Bayesian formulation of incomplete information.�Journal of Economic Theory, 144, 2115-2145.
 Liu, Qingmin (2005), �Representation of belief hierarchies in incomplete information games.�working paper, Stanford University.
 Mertens, Jean-François and Shmuel Zamir (1985), �Formulation of Bayesian analysis for games with incomplete information.� International Journal of Game Theory, 14, 1-29.
 Pearce, David (1984), "Rationalizable strategic behavior and the problem of perfection." Econometrica, 52, 1029-1050.
 Samuelson, Larry and Jianbo Zhang (1989), �Correlated equilibria and mediated equilibria in games with incomplete information.�memeo, Penn State University.
 Shmaya, Eran (2007), "Strongly measurable beliefs." working paper, California Institute of Technology.
 Tang, Qianfeng (2010), "The Bayesian solution and hierarchies of beliefs." working paper.