Abstract
A new framework for equilibrium selection is presented. Playing games recurrently inspace and time may render one of the equilibria “spatially dominant”. Prevailing initially ona large enough finite part of the space, it will take over on the whole space in the long run.In particular it will drive out the other equilibria along travelling waves. This new dominanceconcept is compared with the Harsanyi‐Selten risk‐dominance concept.
Similar content being viewed by others
References
L.E. Blume, The statistical mechanics of best-response strategy revision, Games and Economic Behav. 11(1995)111-145.
H. Carlsson and E. van Damme, Equilibrium selection in stag hunt games, in: Frontiers of Game Theory, eds. K. Binmore, A. Kirman and P. Tani, MIT Press, 1993, pp. 237-253.
R. Cressman and G.T. Vickers, Spatial and density effects in evolutionary game theory, J. Theor. Biol. 184(1997)359-369.
G. Ellison, Learning, local interaction, and coordination, Econometrica 61(1993)1047-1071.
P. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Springer Lecture Notes in Biomathematics 28, 1979.
D. Foster and P. Young, Stochastic evolutionary game dynamics, Theor. Population Biology 38 (1990)219-232.
I. Gilboa and A. Matsui, Social stability and equilibrium, Econometrica 59(1991) 859-867.
W. Güth, Equilibrium selection by unilateral deviation stability, in: Rational Interaction, Essays in Honor of John C. Harsanyi, ed. R. Selten, Springer, Berlin, 1992, pp. 161-189.
W. Güth and B. Kalkofen, Unique Solutions for Strategic Games, Springer Lecture Notes in Economics and Mathematical Systems 328, 1989.
J.C. Harsanyi and R. Selten, A General Theory of Equilibrium Selection in Games, MIT Press, 1988.
J. Hofbauer, Stability for the best response dynamics, Preprint, Vienna, 1994.
J. Hofbauer, Equilibrium selection via travelling waves, in: Yearbook of the Institute Vienna Circle 5/97: Game Theory, Experience, Rationality. Foundations of Social Sciences, Economics and Ethics. In Honor of John C. Harsanyi, eds. W. Leinfellner and E. Koehler, Kluwer, Dordrecht/Boston/London, 1997, pp. 245-260.
J. Hofbauer, V. Hutson and G.T. Vickers, Travelling waves for games in economics and biology, Nonlinear Analysis, TMA 30(1997)1235-1244.
J. Hofbauer and J.W. Weibull, Evolutionary selection against dominated strategies, J. Economic Theory 71(1996)558-573.
V. Hutson and K. Mischaikow, Singular limits for travelling waves for a pair of equations, Proc. Royal Soc. Edinburgh 126A(1996)399-411.
M. Kandori, G.J. Mailath and R. Rob, Learning, mutation and long-run equilibria in games, Econometrica 61(1993)29-56.
Y. Kim, Equilibrium selection in n-person coordination games, Games Economic Behavior 15(1996)203-227.
M. Kosfeld, Stochastic strategy adjustment in coordination games, Preprint, 1996.
B. Kuon, Two-person Bargaining Experiments with Incomplete Information, Springer Lecture Notes in Economics and Mathematical Systems, 1994.
A. Matsui and K. Matsuyama, An approach to equilibrium selection, J. Economic Theory 65(1995)415-434.
K. Mischaikow and V. Hutson, Travelling waves for mutualist species, SIAM J. Math. Anal. 24 (1993)987-1008.
D. Monderer and L. Shapley, Potential games, Games Econ. Behav. 14(1996)124-143.
J. Reineck, Travelling wave solutions to a gradient system, Trans. Amer. Math. Soc. 307(1988)535-544.
L. Samuelson, Evolutionary Games and Equilibrium Selection, MIT Press, 1997.
K. H. Schlag, Why imitate, and if so, how?, Preprint, 1994.
R. Selten, An axiomatic theory of a risk dominance measure for bipolar games with linear incentives, Games Economic Behavior 8(1995)213-263.
R. Sugden, The coexistence of conventions, J. Economic Behavior Organization 28(1995)241-256.
E. van Damme, Equilibrium selection in team games, in: Understanding Strategic Behavior: Essays in Honor of Reinhard Selten, ed. W. Güth, Springer, 1996.
A.I. Volpert, V.A. Volpert and V.A. Volpert, Traveling Wave Solutions of Parabolic Systems, Translations of Mathematical Monographs, Vol. 140, American Mathematical Society, Providence, RI, 1994.
J. W. Weibull, Evolutionary Game Theory, MIT Press, 1995.
Y. Yegorov, Spatial price dynamics, Preprint, 1997.
H.P. Young, The evolution of conventions, Econometrica 61(1993)57-84.
Rights and permissions
About this article
Cite this article
Hofbauer, J. The spatially dominant equilibrium of a game. Annals of Operations Research 89, 233–251 (1999). https://doi.org/10.1023/A:1018979708014
Issue Date:
DOI: https://doi.org/10.1023/A:1018979708014