Oyama, Daisuke and Takahashi, Satoru and Hofbauer, Josef (2003): Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics.
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This paper studies a dynamic adjustment process in a large society of forward-looking agents where payoffs are given by a normal form supermodular game. The stationary states of the dynamics correspond to the Nash equilibria of the stage game. It is shown that if the stage game has a monotone potential maximizer, then the corresponding stationary state is uniquely linearly absorbing and globally accessible for any small degree of friction. Among binary supermodular games, a simple example of a unanimity game with three players is provided where there are multiple globally accessible states for a small friction.
|Item Type:||MPRA Paper|
|Original Title:||Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics|
|Keywords:||equilibrium selection; perfect foresight dynamics; supermodular game; strategic complementarity; stochastic dominance; potential; monotone potential|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
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:||13. Jan 2008 14:54|
|Last Modified:||14. Apr 2015 02:02|
Athey, S. (2001). "Single Crossing Properties and the Existence of Pure Strategy Equlibria in Games of Incomplete Information," Econometrica 69, 861-890.
Aubin, J.-P. and A. Cellina (1984). Differential Inclusions, Springer-Verlag, Berlin.
Carlsson, H. and E. van Damme (1993). "Global Games and Equilibrium Selection," Econometrica 61, 989-1018.
Cooper, R. (1999). Coordination Games: Complementarities and Macroeconomics, Cambridge University Press, Cambridge.
Frankel, D. M., S. Morris, and A. Pauzner (2003). "Equilibrium Selection in Global Games with Strategic Complementarities," Journal of Economic Theory 108, 1-44.
Gilboa, I. and A. Matsui (1991). "Social Stability and Equilibrium,” Econometrica 59, 859-867.
Harsanyi, J. C. and R. Selten (1988). A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge.
Hofbauer, J. (1999). "The Spatially Dominant Equilibrium of a Game,” Annals of Operations Research 89, 233-251.
Hofbauer, J. and W. H. Sandholm (2002). "On the Global Convergence of Stochastic Fictitious Play," Econometrica 70, 2265-2294.
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 (1995). "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory 65, 383-414.
Kaneda, M. (1995). "Industrialization under Perfect Foresight: A World Economy with a Continuum of Countries," Journal of Economic Theory 66, 437-462.
Kim, Y. (1996). "Equilibrium Selection in n-Person Coordination Games,” Games and Economic Behavior 15, 203-227.
Kojima, F. (2003). "Risk-Dominance and Perfect Foresight Dynamics in N-Player Games," forthcoming in Journal of Economic Theory.
Matsui, A. and K. Matsuyama (1995). "An Approach to Equilibrium Selection," Journal of Economic Theory 65, 415-434.
Matsui, A. and D. Oyama (2002). "Rationalizable Foresight Dynamics," forthcoming in Games and Economic Behavior.
Matsuyama, K. (1991). "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," Quarterly Journal of Economics 106, 617-650.
Matsuyama, K. (1992). "The Market Size, Entrepreneurship, and the Big Push," Journal of the Japanese and International Economies 6, 347-364.
Milgrom, P. and J. Roberts (1990). "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica 58, 1255-1277.
Morris, S. (1999). "Potential Methods in Interaction Games,” mimeo.
Morris, S. and H. S. Shin (2003). "Global Games: Theory and Applications," in M. Dewatripont, L. P. Hansen, and S. J. Turnovsky, eds., Advances in Economics and Econometrics: Theory and Applications: Eighth World Congress, Volume 1, Cambridge University Press, Cambridge.
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.
Selten, R. (1995). "An Axiomatic Theory of a Risk Dominance Measure for Bipolar Games with Linear Incentives," Games and Economic Behavior 8, 213-263.
Smith, H. L. (1995). Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, American Mathematical Society, Providence.
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.
Topkis, D. (1979). "Equilibrium Points in Nonzero-Sum n-Person Submodular Games," SIAM Journal on Control and Optimization 17, 773-787.
Vives, X. (1990). "Nash Equilibrium with Strategic Complementarities," Journal of Mathematical Economics 19, 305-321.
Walter, W. (1970). Differential and Integral Inequalities, Spinger-Verlag, Berlin.
Young, P. (1993). "The Evolution of Conventions," Econometrica 61, 57-84.