Oyama, Daisuke and Tercieux, Olivier (2004): Iterated Potential and Robustness of Equilibria.
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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|
|Original Title:||Iterated Potential and Robustness of Equilibria|
|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
|Depositing User:||Daisuke Oyama|
|Date Deposited:||27. Mar 2009 14:05|
|Last Modified:||21. Feb 2013 16:48|
Beckmann, M., C. B. McGuire, and C. B. Winsten (1956). Studies in the Economics of Transportation, Yale University Press, New Haven.
Bergemann, D. and S. Morris (2008). "The Role of the Common Prior in Robust Implementation," Journal of the European Economic Association 6, 551-559.
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.
Okada, D. and O. Tercieux (2008). "Log-linear Dynamics and Local Potential," mimeo.
Oyama, D. (2002). "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory 107, 288-310.
Oyama, D. (2006). "Agglomeration under Forward-Looking Expectations: Potentials and Global Stability," mimeo.
Oyama, D., S. Takahashi, and J. Hofbauer (2008). "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Theoretical Economics 3, 155-192.
Rosenthal, R. W. (1973). "A Class of Games Possessing Pure-Strategy Nash Equilibria," International Journal of Game Theory 2, 65-67.
Rubinstein, A. (1989). "The Electronic Mail Game: Strategic Behavior under 'Almost Common Knowledge'," American Economic Review 79, 385-391.
Sandholm, W. H. (2007). "Pigouvian Pricing and Stochastic Evolutionary Implementation," Journal of Economic Theory 132, 47-69.
Slade, M. E. (1994). "What Does an Oligopoly Maximize?," Journal of Industrial Economics 42, 45-61.
Takahashi, S. (2008). "Perfect Foresight Dynamics in Games with Linear Incentives and Time Symmetry," International Journal of Game Theory 37, 15-38.
Tercieux, O. (2006a). "p-Best Response Set," Journal of Economic Theory 131, 45-70.
Tercieux, O. (2006b). "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.
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Iterated Potential and Robustness of Equilibria. (deposited 30. Jan 2007)
- Iterated Potential and Robustness of Equilibria. (deposited 27. Mar 2009 14:05) [Currently Displayed]