Du, Songzi (2009): Correlated Equilibrium via Hierarchies of Beliefs.

PDF
MPRA_paper_16926.pdf Download (245Kb)  Preview 
Abstract
We study a model of correlated equilibrium where every player takes actions based on his hierarchies of beliefs (belief on what other players will do, on what other players believe about others will do, etc.) intrinsic to the game. Our model does away with messages from outside mediator that are usually assumed in the interpretation of correlated equilibrium. We characterize in every finite, complete information game the exact sets of correlated equilibria (both subjective and objective) that can be obtained conditioning on hierarchies of beliefs; the characterizations rely on a novel iterated deletion procedure. If the procedure ends after k rounds of deletion for a correlated equilibrium obtained from hierarchies of beliefs, then players in the equilibrium need to reason to at most kth order beliefs. Further conceptual and geometric properties of the characterizations are studied.
Item Type:  MPRA Paper 

Original Title:  Correlated Equilibrium via Hierarchies of Beliefs 
Language:  English 
Keywords:  game theory; correlated equilibrium; higher order beliefs; purification; intrinsic correlation 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D80  General C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  16926 
Depositing User:  Songzi Du 
Date Deposited:  25. Aug 2009 08:14 
Last Modified:  12. Feb 2013 13:10 
References:  Aumann, R. J. (1974) Subjectivity and Correlation in Randomized Strategies. Journal of Mathematical Economics, Volume 1, Issue 1, pp. 6796. Aumann, R. J., and J. H. Dreze (2008) Rational Expectations in Games. American Economic Review, 98(1), pp. 7286. Bernheim, B. D. (1984) Rationalizable Strategic Behavior. Econometrica, Volume 52, No. 4, pp. 10071028. Brandenburger, A. and E. Dekel (1987) Rationalizability and Correlated Equilibria. Econometrica, Volume 55, No. 6, pp. 13911402. Brandenburger, A. and A. Friedenberg (2008) Intrinsic Correlation in Games. Journal of Economic Theory, Volume 141, Issue 1, pp. 2867. Kohlberg, E. and J. F. Mertens (1986) On the Strategic Stability of Equilibria. Econometrica, Volume 54, No. 5, pp. 10031037. Mertens, J. F., and S. Zamir (1985) Formulation of Bayesian Analysis for Fames with Incomplete Information. International Journal of Game Theory, Volume 14, No. 1, pp. 129. Myerson, R. B. (1997) Dual Reduction and Elementary Games. Games and Economic Behavior, Volume 21, Issue 12, pp. 183202. Pearce, D. G. (1984) Rationalizable Strategic Behavior and the Problem of Perfection. Econometrica, Volume 52, No. 4, pp. 10291050. Peysakhovich, A. (2009) Correlation Without Signals. Memeo. Siniscalchi, M. (2007) Epistemic Game Theory: Beliefs and Types. The New Palgrave Dictionary of Economics, Second Edition. Tan, T. and S. Werlang (1988) The Bayesian Foundations of Solution Concepts of Games. Journal of Economic Theory, Volume 45, Issue 2, pp. 370391. von Stengel, B. (2002) Computing equilibria for twoperson games. Chapter 45, Handbook of Game Theory, Vol. 3, eds. R. J. Aumann and S. Hart, NorthHolland, Amsterdam, pp. 17231759. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/16926 