2002) “On equilibrium in pure strategies in games with many players

¤This paper continues research initiated in Wooders, Cartwright and Selten (2001). We are indebted to Bhaskar Dutta and Ehud Kalai for stimulating and helpful comments. 1 Abstract: 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 su¢ciently 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 at-tributes of players (their external e¤ects on others) and their taste attributes (their payo ¤ 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 …nite number of crowding attributes, we obtain analogs, for …nite games, of puri…cation results due to Pascoa (1993a,b,1998) for games with a continuum of players. Our main theorems are based on a new mathe