Iterated Potential and Robustness of Equilibria

Oyama, Daisuke and Tercieux, Olivier (2004): Iterated Potential and Robustness of Equilibria.

Abstract

For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies such a procedure to define the concept of iterated monotone potential maximizer (iterated MP-maximizer). It is shown that under some monotonicity conditions, an iterated MP-maximizer is robust to incomplete information (Kajii and Morris, Econometrica 65 (1997)) and absorbing and globally accessible under perfect foresight dynamics for a small friction (Matsui and Matsuyama, Journal of Economic Theory 65 (1995)). Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.

• Item Type: MPRA Paper
• Language: English
• Keywords: equilibrium selection; robustness; incomplete information; perfect foresight dynamics; iteration; monotone potential; p-dominance
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; 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 > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

Blume, L. E. (1993). "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior 5, 387-424.

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

Goldstein, I. and A. Pauzner (2005). "Demand-Deposit Contracts and the Probability of Bank Runs," Journal of Finance 60, 1293-1327.

Harsanyi, J. C. and R. Selten (1988). A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge.

Hofbauer, J. and G. Sorger (1999). "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory 85, 1-23.

Hofbauer, J. and G. Sorger (2002). "A Differential Game Approach to Evolutionary Equilibrium Selection," International Game Theory Review 4, 17-31.

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

Kandori, M., G. J. Mailath, and R. Rob (1993). "Learning, Mutation, and Long Run Equilibria in Games," Econometrica 61, 29-56.

Kandori, M. and R. Rob (1998). "Bandwagon Effects and Long Run Technology Choice," Games and Economic Behavior 22, 30-60.

Kim, Y. (1996). "Equilibrium Selection in n-Person Coordination Games," Games and Economic Behavior 15, 203-227.

Kohlberg, E. and J.-F. Mertens (1986). "On the Strategic Stability of Equilibria," Econometrica 54, 1003-1037.

Kojima, F. (2006). "Risk-Dominance and Perfect Foresight Dynamics in N-Player Games," Journal of Economic Theory 128, 255-273.

Matsui, A. and K. Matsuyama (1995). "An Approach to Equilibrium Selection," Journal of Economic Theory 65, 415-434.

Matsui, A. and D. Oyama (2006). "Rationalizable Foresight Dynamics," Games and Economic Behavior 56, 299-322.

Matsuyama, K. (1991). "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," Quarterly Journal of Economics 106, 617-650.

Matsuyama, K. (1992a). "A Simple Model of Sectoral Adjustment," Review of Economic Studies 59, 375-388.

Matsuyama, K. (1992b). "The Market Size, Entrepreneurship, and the Big Push," Journal of the Japanese and International Economies 6, 347-364.

Monderer, D. and L. Shapley (1996). "Potential Games," Games and Economic Behavior 14, 124-143.

Morris, S. (1999). "Potential Methods in Interaction Games," mimeo.

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

Morris, S. and H. S. Shin (1998). "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review 88, 587-597.

Morris, S. and T. Ui (2005). "Generalized Potentials and Robust Sets of Equilibria," Journal of Economic Theory 124, 45-78.

Oyama, D. (2002). "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory 107, 288-310.

Oyama, D., S. Takahashi, and J. Hofbauer (2003). "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," mimeo.

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

Takahashi, S. (2005). "Perfect Foresight Dynamics in Games with Linear Incentives and Time Symmetry," mimeo.

Tercieux, O. (2004). "p-Best Response Set," forthcoming in Journal of Economic Theory.

Tercieux, O. (2006). "p-Best Response Set and the Robustness of Equilibria to Incomplete Information," Games and Economic Behavior 56, 371-384.

Ui, T. (2001). "Robust Equilibria of Potential Games," Econometrica 69, 1373-1380.

Young, P. (1993). "The Evolution of Conventions," Econometrica 61, 57-84.