All-Stage strong correlated equilbrium

Heller, Yuval (2008): All-Stage strong correlated equilbrium.

Abstract

A strong correlated equilibrium is a strategy profile that is immune to joint deviations. Different notions of strong correlated equilibria were defined in the literature. One major difference among those definitions is the stage in which coalitions can plan a joint deviation: before (ex-ante) or after (ex-post) the deviating players receive their part of the correlated profile. In this paper we prove that if deviating coalitions are allowed to use new correlating devices, then an ex-ante strong correlated equilibrium is immune to deviations at all stages. Thus the set of ex-ante strong correlated equilibria of Moreno & Wooders (1996) is included in all other sets of strong correlated equilibria.

• Item Type: MPRA Paper
• Language: English
• Keywords: coalition-proofness, strong correlated equilibrium, common knowledge, incomplete information, noncooperative games
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Abraham I., Dolev D., Gonen R., Halpern J., 2006. Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. Proceedings of the 25th annual ACM symposium on principles of distributed computing, 53-62.

Aumann, R.,1959. Acceptable Points in General cooperative n-person Games, in Kuhn H.W., Luce R.D. (Eds.), Contributions to the Theory of Games IV. Princeton University Press, NJ, 287-324.

Aumann, R., 1976. Agreeing to disagree. Ann. Statist. 4 (no. 6), 1236-1239.

Aumann, R., 1987. Correlated equilibrium as an expression of Bayesian rationality, Econometrica 55, 1-18.

Aumann R., Hart, S., 2003. Long cheap talk. Econometrica 71 (6), 1619-1660.

Bernheim, B.D., Whinston, M., 1986. Menu auctions, resource allocation, and economic influence, Quart. J. Econom. 101, 1-31.

Bernheim, B.D., Peleg, B., Whinston, M., 1987. Coalition-proof Nash equilibria - I. concepts. J. Econ. Theory 42, 1-12.

Bernheim, B.D., Whinston, M., 1987. Coalition-proof Nash equilibria - II. applications. J. Econ. Theory 42, 13-29.

Bloch F., Dutta B., 2007. Correlated equilibria, incomplete information and coalitional deviations. mimeo (based on The Warwick Economics Research Paper Series - paper 763).

Chwe, MS-Y, 1994. Farsighted coalitional stability. J. Econ. Theory 63, 299-325.

Delgado J., Moreno D., 2004. Coalition-proof supply function equilibria in Oligopoly. J. Econ. Theory, 114 231-254.

Einy, E., Peleg B., 1995. Coalition-proof communication equilibria, in Social Choice, Welfare & Ethics (W. Barnett, H. Moulin, M. Salles and N. Schofield, eds.), Cambridge, New-York and Melbourne: Cambridge University Press.

Farrel J., Rabin M., 1996. Cheap-talk, J. Econ. Perspect. 10, 103-118.

Farrel, J., Saloner, G., 1988. Coordination through committees and markets. RAND J. Econ. 19, 235-252.

Greenberg, J., 1989. Deriving strong and coalition-prof Nash equilibrium from an abstract system. J. Econ. Theory 49, 195-202.

Greenberg, J., 1990. The theory of social situations. Cambridge University Press.

Heller Y., 2008, A Minority-proof cheap-talk protocol, mimeo, http://www.tau.ac.il/ ̃helleryu/minority.pdf

Holzman R., Law-Yone N., 1997. Strong equilibrium in congestion games, Games Econ. Behav. 21, 85-101.

Konishi, H., Le Breton, M.,Weber, S., 1997a. Equilibria in a model with partial rivalry. J. Econ. Theory 72, 225-237.

Konishi, H., Le Breton, M.,Weber, S., 1997b. Equivalence of strong and coalition-proof Nash equilibria in games without spillovers. Econ. Theory 9, 97-113.

Konishi, H., Le Breton, M.,Weber, S., 1999. On coalition-proof Nash Equilibria in common agency games. J. Econ. Theory 85, 122-139.

Lepinski, M., Micali, S., Peikert C., Shelat A., 2004. Completely fair SFE and coalition-Safe cheap talk. Proceedings of the 23rd annual ACM symposium on Principles of distributed computing, 1-10.

Mariotti, M., 1997. A theory of agreements in strategic form games. J. Econ. Theory 74, 196-217.

Milgrom, P., Roberts, J., 1996. Coalition-proofness and correlation with arbitrary communication possibilities, Games Econ. Behav. 17, 113-128.

Moreno, D., Wooders, J., 1996. Coalition-proof equilibrium, Games Econ. Behav. 17, 80-113.

Moreno, D., Wooders, J., 1998. An experimental study of communication and coordination in non-cooperative Games, Games Econ. Behav. 24, 47-76.

Rabin, M., 1994. A model of pre-game communication. J. Econ. Theory 63, 370-391.

Ray I., 1996. Coalition-proof correlated equilibrium: a definition, Games Econ. Behav. 17, 56-79.

Ray, I., 1998. Correlated equilibrium as a stable standard of behavior, Rev. Econ. Design 3, 257-269

Thoron, S., 1998. Formation of a Coalition-Proof Stable Cartel, Economics Can. J. Econ. 31, 63-76.

Von-Neumann, J., Morgenstern O., 1953. Theory of games and economic behavior. 3rd ed., Princeton University Press, NJ.

Xue, L., 1998. Coalitional stability under perfect foresight. Econ. Theory 11, 603-627.

Xue, L., 2000. Negotiation-proof Nash equilibrium. Int. J. Game Theory 29, 339-357.

Yi SS., 1999. On the coalition-proofness of the Pareto frontier of the set of Nash equilibria, Games Econ. Behav. 26 353-364.