zbMATH — the first resource for mathematics

Perfect foresight and equilibrium selection in symmetric potential games. (English) Zbl 0922.90146
Summary: The equilibrium selection approach of A. Matsui and K. Matsuyama [J. Econ. Theory 65, No. 2, 415-434 (1995; Zbl 0835.90121)] which is based on rational players who maximize their discounted future payoff, is analyzed for symmetric two-player games with a potential function. It is shown that the maximizer of the potential function is the unique state that is absorbing and globally accessible for small discount rates. \(\copyright\) Academic Press.

91A05 2-person games
Full Text: DOI
[1] Alós-Ferrer, C., Dynamical Systems with a Continuum of Randomly Matched Agents, Working Paper 9801, (1998), University of ViennaDepartment of Economics
[2] Aubin, J. P.; Cellina, A., Differential Inclusions, (1984), Springer-Verlag Berlin
[3] Baum, D. F., Existence theorems for Lagrange control problems with unbounded time domain, J. Opt. Theory Appl., 19, 89-116, (1976) · Zbl 0305.49002
[4] Carlsson, H.; van Damme, E., Global games and equilibrium selection, Econometrica, 61, 989-1018, (1993) · Zbl 0794.90083
[5] Clarke, F. H., Optimization and Nonsmooth Analysis, (1983), Wiley New York · Zbl 0727.90045
[6] Harsanyi, J. C.; Selten, R., A General Theory of Equilibrium Selection in Games, (1988), MIT Press Cambridge · Zbl 0693.90098
[7] J. Hofbauer, Stability for the best response dynamics, Department of Mathematics, University of Vienna, 1995
[8] Hofbauer, J., Equilibrium selection via travelling waves, Vienna Circle Institute Yearbook 5/97: Game Theory, Experience, Rationality. Foundations of Social Sciences, Economics, and Ethics. In Honor of John C. Harsanyi, (1998), Kluwer Dordrecht-Boston-London, p. 245-259 · Zbl 0995.91005
[9] Hofbauer, J.; Sigmund, K., The Theory of Evolution and Dynamical Systems, (1988), Cambridge Univ. Press Cambridge
[10] Matsui, A.; Matsuyama, K., An approach to equilibrium selection, J. Econ. Theory, 65, 415-434, (1995) · Zbl 0835.90121
[11] Kandori, M.; Mailath, G. J.; Rob, R., Learning, mutation, and long run equilibria in games, Econometrica, 61, 29-56, (1993) · Zbl 0776.90095
[12] Kandori, M.; Rob, R., Evolution of equilibria in the long run: a general theory and applications, J. Econ. Theory, 65, 383-414, (1995) · Zbl 0837.90139
[13] Maynard Smith, J., Evolution and the Theory of Games, (1982), Cambridge Univ. Press Cambridge · Zbl 0526.90102
[14] Monderer, D.; Shapley, L., Potential games, Games Econ. Behav., 14, 124-143, (1996) · Zbl 0862.90137
[15] Monderer, D.; Shapley, L., Fictitious play property for games with identical interests, J. Econ. Theory, 68, 258-265, (1996) · Zbl 0849.90130
[16] Robson, A. J.; Vega-Redondo, F., Efficient equilibrium selection in evolutionary games with random matching, J. Econ. Theory, 70, 65-92, (1996) · Zbl 0859.90138
[17] Scheinkman, J. A., On optimal steady states ofn, J. Econ. Theory, 12, 11-30, (1976) · Zbl 0341.90017
[18] Seierstad, A., Dynamic Programming Approach to Infinite Horizon Deterministic Continuous Time Control Problems, (1997), University of OsloDepartment of Economics
[19] Seierstad, A.; Sydsaeter, K., Optimal Control Theory with Economic Applications, (1987), North-Holland Amsterdam · Zbl 0613.49001
[20] van Damme, E., Equilibrium selection in team games, (Güth, W., Understanding Strategic Behavior: Essays in Honor of Reinhard Selten, (1996), Springer-Verlag Berlin) · Zbl 0874.90205
[21] Van Huyck, J.; Battalio, R.; Beil, R., Tactic coordination games, strategic uncertainty, and coordination failure, Amer. Econ. Rev., 80, 234-248, (1990)
[22] Weibull, J. W., Evolutionary Game Theory, (1995), MIT Press Cambridge · Zbl 0879.90206
[23] Young, H. P., The evolution of conventions, Econometrica, 61, 57-84, (1993) · Zbl 0773.90101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.