On the Strategic Impact of an Event under Non-Common Priors

Oyama, Daisuke and Tercieux, Olivier (2005): On the Strategic Impact of an Event under Non-Common Priors.

Abstract

This paper studies the impact of a small probability event on strategic behavior in incomplete information games with non-common priors. It is shown that the global impact of a small probability event (i.e., its propensity to affect strategic behavior at all states in the state space) has an upper bound that is an increasing function of a measure of discrepancy from the common prior assumption. In particular, its global impact can be arbitrarily large under non-common priors, but is bounded from above under common priors. These results quantify the different implications common prior and non-common prior models have on the (infinite) hierarchies of beliefs.

• Item Type: MPRA Paper
• Language: English
• Keywords: common prior assumption; higher order belief; rationalizability; contagion; belief potential
• 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

Aumann, R. J. (1976). ``Agreeing to Disagree,'' Annals of Statistics 4, 1236-1239.

Battigalli, P. and M. Siniscalchi (2003). ``Rationalization and Incomplete Information,'' Advances in Theoretical Economics 3, Article 3, 1-44.

Brandenburger, A. and E. Dekel (1993). ``Hierarchies of Beliefs and Common Knowledge,'' Journal of Economic Theory 59, 189-198.

Carlsson, H. and E. van Damme (1993). ``Global Games and Equilibrium Selection,'' Econometrica 61, 989-1018.

Dekel, E., D. Fudenberg, and S. Morris (2007). ``Interim Correlated Rationalizability,'' Theoretical Economics 2, 15-40.

Kajii, A. and S. Morris (1997). ``The Robustness of Equilibria to Incomplete Information,'' Econometrica 65, 1283-1309.

Lipman, B. L. (2003). ``Finite Order Implications of Common Priors,'' Econometrica 71, 1255-1267.

Lipman, B. L. (2005). ``Finite Order Implications of Common Priors in Infinite Models,'' mimeo.

Mertens, J.-F. and S. Zamir (1985). ``Formulation of Bayesian Analysis for Games with Incomplete Information,'' International Journal of Game Theory 14, 1-29.

Milgrom, P. and N. Stokey (1982). ``Information, Trade, and Common Knowledge,'' Journal of Economic Theory 26, 17-27.

Monderer, D. and D. Samet (1989). ``Approximating Common Knowledge with Common Beliefs,'' Games and Economic Behavior 1, 170-190.

Morris, S., R. Rob, and H. S. Shin (1995). ``p-Dominance and Belief Potential,'' Econometrica 63, 145-157.

Oyama, D. and O. Tercieux (2005). ``Robust Equilibria under Non-Common Priors,'' mimeo.

Rubinstein, A. (1989). ``The Electronic Mail Game: Strategic Behavior under `Almost Common Knowledge','' American Economic Review 79, 385-391.

Weinstein, J. and M. Yildiz (2007). ``A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements,'' Econometrica 75, 365-400.

Yildiz, M. (2004). ``Generic Uniqueness of Rationalizable Actions,'' mimeo.