On Equilibrium in Pure Strategies in Games with Many Players

Edward Cartwright and Myrna Wooders

No 511, Vanderbilt University Department of Economics Working Papers from Vanderbilt University Department of Economics

Abstract: Treating games of incomplete information with countable sets of actions and types and finite but large player sets we demonstrate that for every mixed strategy profile there is a pure strategy profile that is 'epsilon-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 and any other attributes that are not directly relevant to other players). The main assumption is a 'large game' property, dictating that the actions of relatively small subsets of players cannot have large effects on the payoffs of others Since it is well known that, even allowing mixed strategies, with a countable set of actions a Nash equilibrium may not exist, we provide an existence of equilibrium theorem. The proof of existence relies on a relationship between the 'better reply security' property of Reny (1999) and a stronger version of the large game property. Our purification theorem are based on a new mathematical result, of independent interest, applicable to countable strategy spaces.

Keywords: Noncooperative games; incomplete information; purification; crowding attributes; large game property; countable action set; better reply security (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2005-04
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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http://www.accessecon.com/pubs/VUECON/vu05-w11.pdf First version, 2005 (application/pdf)

Related works:
Journal Article: On equilibrium in pure strategies in games with many players (2009)
Working Paper: On Equilibrium in Pure Strategies in Games with Many Players (2003)
Working Paper: On Equilibrium in Pure Strategies in Games with Many Players (2003)
Working Paper: On Equilibrium in Pure Stategies in Games with Many Players (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:van:wpaper:0511

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