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Social conformity and equilibrium in pure strategies in games with many players
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Wooders, Myrna Holtz, Cartwright, Edward and Selten, Reinhard (2002) Social conformity and equilibrium in pure strategies in games with many players. Working Paper. Coventry: University of Warwick, Department of Economics. (Warwick economic research papers).

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Abstract
We introduce a framework of noncooperative pregames, in which players are characterized by their attributes, and demonstrate that for all games with sufficiently many players, there exist approximate (e )Nash equilibria in pure strategies. In fact, every mixed strategy equilibrium can be used to construct an eequilibrium in pure strategies, an ‘e purification’ result. Our main result is a social conformity theorem. Interpret a set of players, all with attributes in some convex subset of attribute space and all playing the same strategy, as a society. Observe that the number of societies may be as large as the number of players. Our social conformity result dictates that, given e > 0, there is an integer L, depending on e but not on the number of players, such that any suffciently large game has an e equilibrium in pure strategies that induces a partition of the player set into fewer than L societies.
Item Type:  Working or Discussion Paper (Working Paper) 

Alternative Title:  Original version, May 15, 2001; this version, April 2002 
Subjects:  H Social Sciences > HB Economic Theory H Social Sciences > HM Sociology 
Divisions:  Faculty of Social Sciences > Economics 
Library of Congress Subject Headings (LCSH):  Noncooperative games (Mathematics), Conformity, Games of strategy (Mathematics), Group theory, Game theory 
Series Name:  Warwick economic research papers 
Publisher:  University of Warwick, Department of Economics 
Place of Publication:  Coventry 
Date:  April 2002 
Number:  No.636 
Number of Pages:  59 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
Version or Related Resource:  Revised version of: Wooders, M.H., Cartwright, E. and Selten, R. (2001). Some first results for noncooperative pregames: social conformity and equilibrium in pure strategies. [Coventry] : University of Warwick, Economics Department. (Warwick economic research papers, no.589). 
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URI:  http://wrap.warwick.ac.uk/id/eprint/1554 
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