On equilibrium in pure strategies in games with many players
Cartwright, Edward and Wooders, Myrna Holtz (2003) On equilibrium in pure strategies in games with many players. Working Paper. Coventry: University of Warwick, Department of Economics. Warwick economic research papers (No.686).
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We introduce a framework of noncooperative games, allowing both countable sets of pure strategies and player types, in which players are characterized by their attributes and demonstrate that for all games with sufficiently many players, every mixed strategy Nash equilibrium can be used to construct a Nash "-equilibrium in pure strategies that is ‘"-equivalent’. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functions). The set of crowding attributes is assumed to be compact; this is not required, however, for taste attributes. For the special case of at most a finite number of crowding attributes, we obtain analogs, for finite games, of purification results due to Pascoa (1993a,b,1998) for games with a continuum of players. Our main theorems are based on a new mathematical result, in the spirit of the Shapley-Folkman Theorem but applicable to a countable (not necessarily finite dimensional) strategy space.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HB Economic Theory|
|Divisions:||Faculty of Social Sciences > Economics|
|Library of Congress Subject Headings (LCSH):||Noncooperative games (Mathematics), Group theory, Game theory, Statistical decision, Strategy (Philosophy)|
|Series Name:||Warwick economic research papers|
|Publisher:||University of Warwick, Department of Economics|
|Place of Publication:||Coventry|
|Official Date:||26 October 2003|
|Number of Pages:||37|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
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