The games of type considered in the present paper (LSE-games) extend the concept of LSF-games studied by Wieczorek in [2004], both types of games being related to games with a continuum of players. LSE-games can be seen as anonymous games with finitely many types of players, their action sets included in Euclidean spaces and payoffs depending on a player's own action and finitely many integral characteristics of distributions of the players' (of all types) actions. We prove the existence of equilibria and present a minimization problem and a complementarity problem (both nonlinear) whose solutions are exactly the same as equilibria in the given game. Examples of applications include a model of social adaptation and a model of economic efficiency enforced by taxation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-6,
author = {Andrzej Wieczorek},
title = {Large games with only small players and strategy sets in Euclidean spaces},
journal = {Applicationes Mathematicae},
volume = {32},
year = {2005},
pages = {183-193},
zbl = {1178.91021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-6}
}
Andrzej Wieczorek. Large games with only small players and strategy sets in Euclidean spaces. Applicationes Mathematicae, Tome 32 (2005) pp. 183-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-6/