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On Equilibrium in Pure Strategies in Games with Many Players Author info | Abstract | Publisher info | Download info | Related research | Statistics Edward Cartwright () (Department of Economics, Keynes College, University of Kent)
Myrna Wooders () (Department of Economics, Vanderbilt University)
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registered author(s):
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.
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Paper provided by Department of Economics, Vanderbilt University in its series Working Papers with number
0511.
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Date of creation: Apr 2005Date of revision:
Handle: RePEc:van:wpaper:0511Contact details of provider: Postal: Box 1819, Station B, Nashville, TN 37235 Fax: 615-343-8495 Email: Web page: http://sitemason.vanderbilt.edu/econ/ More information through EDIRC
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Keywords: Noncooperative games ; incomplete information ; purification ; crowding attributes ; large game property ; countable action set ; better reply security ; Other versions of this item:
Find related papers by JEL classification: C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports :
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile , click on "citations" and make appropriate adjustments.: Edward Cartwright & Myrna Wooders, 2003.
"On Equilibrium in Pure Strategies in Games with Many Players ,"
Working Papers
2003.122, Fondazione Eni Enrico Mattei.
[Downloadable!]
Other versions:
Edward Cartwright & Myrna Wooders, 2005.
"On Equilibrium in Pure Strategies in Games with Many Players ,"
Working Papers
0511, Department of Economics, Vanderbilt University.
[Downloadable!] Cartwright, Edward & Wooders, Myrna, 2003.
"On Equilibrium in Pure Stategies in Games with Many Players ,"
The Warwick Economics Research Paper Series (TWERPS)
686, University of Warwick, Department of Economics.
[Downloadable!] Edward Cartwright & Myrna Wooders, 2009.
"On equilibrium in pure strategies in games with many players ,"
International Journal of Game Theory ,
Springer, vol. 38(1), pages 137-153, March.
[Downloadable!] (restricted) Edward Cartwright & Myrna Wooders, 2005.
"On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium ,"
Working Papers
0512, Department of Economics, Vanderbilt University.
[Downloadable!]
Other versions:
Cartwright, Edward & Wooders, Myrna, 2004.
"On Purification Of Equilibrium In Bayesian Games And Ex-Post Nash Equilibrium ,"
The Warwick Economics Research Paper Series (TWERPS)
701, University of Warwick, Department of Economics.
[Downloadable!] Edward Cartwright & Myrna Wooders, 2009.
"On purification of equilibrium in Bayesian games and expost Nash equilibrium ,"
International Journal of Game Theory ,
Springer, vol. 38(1), pages 127-136, March.
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Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2006.
"Behavioral conformity in games with many players ,"
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"Continuum and Finite-Player Noncooperative Models of Competition ,"
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Other versions: Kovalenkov, Alexander & Wooders, Myrna, 2003.
"Approximate cores of games and economies with clubs ,"
Journal of Economic Theory ,
Elsevier, vol. 110(1), pages 87-120, May.
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Alexander Kovalenkov & Myrna H. Wooders, 1998.
"Approximate cores of games and economies with clubs ,"
Working Papers
mwooders-00-01, University of Toronto, Department of Economics.
[Downloadable!] Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999.
"Approximate Cores Of Games And Economies With Clubs ,"
The Warwick Economics Research Paper Series (TWERPS)
535, University of Warwick, Department of Economics.
[Downloadable!] Kovalenkov, Alexander & Wooders, Myrna Holtz, 2002.
"Approximate Cores Of Games And Economies With Clubs ,"
The Warwick Economics Research Paper Series (TWERPS)
634, University of Warwick, Department of Economics.
[Downloadable!] Alexander Kovalenkov & Myrna Holtz Wooders, 2000.
"Approximate Cores of Games and Economies with Clubs ,"
Econometric Society World Congress 2000 Contributed Papers
1790, Econometric Society.
[Downloadable!]
Full
references Cited by : (explanations , Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile , click on "citations" and make appropriate adjustments.)
Edward Cartwright & Myrna Wooders, 2009.
"On equilibrium in pure strategies in games with many players ,"
International Journal of Game Theory ,
Springer, vol. 38(1), pages 137-153, March.
[Downloadable!] (restricted)
Other versions:
Edward Cartwright & Myrna Wooders, 2005.
"On Equilibrium in Pure Strategies in Games with Many Players ,"
Working Papers
0511, Department of Economics, Vanderbilt University.
[Downloadable!] Edward Cartwright & Myrna Wooders, 2003.
"On Equilibrium in Pure Strategies in Games with Many Players ,"
Working Papers
2003.122, Fondazione Eni Enrico Mattei.
[Downloadable!] Cartwright, Edward & Wooders, Myrna, 2003.
"On Equilibrium in Pure Stategies in Games with Many Players ,"
The Warwick Economics Research Paper Series (TWERPS)
686, University of Warwick, Department of Economics.
[Downloadable!] Edward Cartwright & Myrna Wooders, 2009.
"On purification of equilibrium in Bayesian games and expost Nash equilibrium ,"
International Journal of Game Theory ,
Springer, vol. 38(1), pages 127-136, March.
[Downloadable!] (restricted)
Other versions:
Cartwright, Edward & Wooders, Myrna, 2004.
"On Purification Of Equilibrium In Bayesian Games And Ex-Post Nash Equilibrium ,"
The Warwick Economics Research Paper Series (TWERPS)
701, University of Warwick, Department of Economics.
[Downloadable!] Edward Cartwright & Myrna Wooders, 2005.
"On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium ,"
Working Papers
0512, Department of Economics, Vanderbilt University.
[Downloadable!]
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