Oyama, Daisuke and Tercieux, Olivier (2005): Robust Equilibria under Non-Common Priors.
This is the latest version of this item.
Download (343kB) | Preview
This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogenous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.
|Item Type:||MPRA Paper|
|Original Title:||Robust Equilibria under Non-Common Priors|
|Keywords:||incomplete information; robustness; common prior assumption; higher order belief|
|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
|Depositing User:||Daisuke Oyama|
|Date Deposited:||27. Mar 2009 03:10|
|Last Modified:||17. Feb 2013 20:20|
Aumann, R. J. (1974). ``Subjectivity and Correlation in Randomized Strategies,'' Journal of Mathematical Economics 1, 67-96.
Aumann, R. J. (1987). ``Correlated Equilibrium as an Expression of Bayesian Rationality,'' Econometrica 55, 1-18.
Battigalli, P. and M. Siniscalchi (2003). ``Rationalization and Incomplete Information,'' Advances in Theoretical Economics 3, Article 3, 1-44.
Brandenburger, A. and E. Dekel (1987). ``Rationalizability and Correlated Equilibria,'' Econometrica 55, 1391-1402.
Brandenburger, A. and E. Dekel (1993). ``Hierarchies of Beliefs and Common Knowledge,'' Journal of Economic Theory 59, 189-198.
Dekel, E., D. Fudenberg, and D. Levine (2004). ``Learning to Play Bayesian Games,'' Games and Economic Behavior 46, 282-303.
Dekel, E., D. Fudenberg, and S. Morris (2007). ``Interim Correlated Rationalizability,'' Theoretical Economics 2, 15-40.
Fudenberg, D., D. Kreps, and D. Levine (1988). ``On the Robustness of Equilibrium Refinements,'' Journal of Economic Theory 44, 354-380.
Harsanyi, J. C. (1973). ``Games with Randomly Disturbed Payoffs: A New Rationale for Mixed-Strategy Equilibrium Points,'' International Journal of Game Theory 2, 1-23.
Kajii, A. and S. Morris (1997). ``The Robustness of Equilibria to Incomplete Information,'' Econometrica 65, 1283-1309.
Kohlberg, E. and J.-F. Mertens (1986). ``On the Strategic Stability of Equilibria,'' Econometrica 54, 1003-1037.
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.
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.
Morris, S. and T. Ui (2005). ``Generalized Potentials and Robust Sets of Equilibria,'' Journal of Economic Theory 124, 45-78.
Oyama, D. and O. Tercieux (2004). ``Iterated Potential and Robustness of Equilibria,'' forthcoming in Journal of Economic Theory.
Oyama, D. and O. Tercieux (2005). ``On the Strategic Impact of an Event under Non-Common Priors,'' mimeo.
Ui, T. (2001). ``Robust Equilibria of Potential Games,'' Econometrica 69, 1373-1380.
Weinstein, J. and M. Yildiz (2004). ``Finite-Order Implications of Any Equilibrium,'' MIT Department of Economics Working Paper 04-06.
Weinstein, J. and M. Yildiz (2007). ``A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements,'' Econometrica 75, 365-400.
Available Versions of this Item
Robust Equilibria under Non-Common Priors. (deposited 14. Mar 2008 09:12)
- Robust Equilibria under Non-Common Priors. (deposited 27. Mar 2009 03:10) [Currently Displayed]