The paper deals with the question of existence and properties of equilibrated distributions of individual characteristics in an infinite population. General game-theoretic methods are applied and special attention is focused on the case of fitness functions depending only on the distance of an individual characteristic from a reference point and from the mean characteristics. Iterative procedures leading to equilibrated distributions are also considered.
@article{bwmeta1.element.bwnjournal-article-zmv25i4p417bwm,
author = {A. Wieczorek and A. Wiszniewska},
title = {A game-theoretic model of social adaptation in an infinite population},
journal = {Applicationes Mathematicae},
volume = {26},
year = {1999},
pages = {417-430},
zbl = {1050.91505},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i4p417bwm}
}
Wieczorek, A.; Wiszniewska, A. A game-theoretic model of social adaptation in an infinite population. Applicationes Mathematicae, Tome 26 (1999) pp. 417-430. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i4p417bwm/
[000] [1] E. Balder, A unifying approach to existence of Nash equilibria, Internat. J. Game Theory 24 (1995), 79-94. | Zbl 0837.90137
[001] [2] C. Berge, Espaces topologiques. Fonctions multivoques, Dunod, 1959. | Zbl 0088.14703
[002] [3] M. L. Cody and J. M. Diamond (eds.), Ecology and Evolution of Communities, Harvard Univ. Press, 1975.
[003] [4] J. M. Diamond and T. J. Case (eds.), Community Ecology, Harper and Row, 1986.
[004] [5] J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, Cambridge Univ. Press, 1988. | Zbl 0678.92010
[005] [6] A. Kacelnik, J. R. Krebs and C. Bernstein, The ideal free distribution and predator-prey populations, Trends in Ecology and Evolution 7 (1992), 50-55.
[006] [7] A. Mas-Colell, On a theorem of Schmeidler, J. Math. Econom. 13 (1984), 201-206. | Zbl 0563.90106
[007] [8] I. Milchtaich, Congestion games with player specific payoff functions, Games and Economic Behavior 13 (1996), 101-124. | Zbl 0848.90131
[008] [9] I. Milchtaich, Congestion models of competition, Amer. Naturalist 5 (1996), 760-783.
[009] [10] G. A. Parker and W. J. Sutherland, Ideal free distributions when individuals differ in competitive ability: phenotype limited ideal free models, Animal Behaviour 34 (1986), 1222-1242.
[010] [11] D. Schmeidler, Equilibrium points of nonatomic games, J. Statist. Phys. 17 (1973), 295-300. | Zbl 1255.91031
[011] [12] E. Van Damme, Stability and Perfection of Nash Equilibria, Springer, 1987. | Zbl 0696.90087
[012] [13] A. Wieczorek, Elementary large games and an application to economies with many agents, report 805, Inst. Computer Sci., Polish Acad. Sci., 1996.
[013] [14] A. Wieczorek, Simple large games and their applications to problems with many agents, report 842, Inst. Computer Sci., Polish Acad. Sci., 1997.