Wooders, Myrna Holtz, Selten, Reinhard and Cartwright, Edward (2001) Some first results for noncooperative pregames: social conformity and equilibrium in pure strategies. Working Paper. University of Warwick, Department of Economics, Coventry.

Preview

PDF WRAP_Wooders_twerp589rev.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (431Kb)

Abstract

We introduce the framework of noncooperative pregames 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 E-equilibrium in pure strategies — ours is an 'E-purification’ result. Our main result is that there exists an E-equilibrium in pure strategies with the property that most players choose the same strategies as all other players with similar attributes. More precisely, there is an integer L, depending on E but not on the number of players, so that any sufficiently large society can be partitioned into fewer than L groups, or cultures, consisting of similar players, and all players in the same group play the same pure strategy. In ongoing research, we are extending the model to cover a broader class of situations, including incomplete information. We would be grateful for any comments that might help us improve the paper.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Noncooperative games (Mathematics), Conformity, Social influence, Equilibrium (Economics), Game theory
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	8 August 2001
Number:	No.589
Number of Pages:	42
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Description:	Original version, May 15, 2001; this version, August 8, 2001
Funder:	Sonderforschungsbereich 303 -- "Information und die Koordination wirtschaftlicher Aktivitäten", Universität Bonn
References:	[1] Araujo, A., M. Pascoa and J. Orrillo (2000) “Equilibrium with default and exogenous collateral,” Mathematical Finance. [2] Aumann, R.J., Y. Katznelson, R. Radner, R.W, Rosenthal,and B.Weiss (1983) “Approximate purification of mixed strategies,” Mathematics of Operations Research 8, 327-341. [3] Cartwright, E. and M.Wooders (2001) “Purifying equilibria in Bayesian games derived from noncooperative pregames,” Notes. [4] Follmer, H. (1974) “Random economies with many interacting agents,” Journal of Mathematical Economics 1, 51-62. [5] Green, J. and W.P.Heller (1991) “Mathematical Analysis and Convexity with Applications to Economics,” in Handbook of Mathematical Economics, Vol.1, K.J. Arrow andW. Intriligator, eds. North Holland: Amsterdam, New York, Oxford. [6] Hildenbrand,W. (1971) “Random preferences and equilibriumanalysis,” Journal of Economic Theory 3, 414-429. [7] Kalai, E. (2000) “Private information in large games,” Northwestern University Discussion Paper 1312. [8] Khan, A. (1989) “On Cournot-Nash equilibrium distributions for games with a nonmetrizable action space and upper semi continuous payoffs,” Transactions of the American Mathematical Society 293: 737-749. [9] Khan, A., K.P.Rath and Y.N.Sun (1997) “On the existence of pure strategy equilibria with a continuum of players,” Journal of Economic Theory 76:13-46. [10] Kirman, A.P. (1981) “Measure Theory,” Handbook of Mathematical Economics, K. Arrow and M. Intrilligator (eds.), North Holland Amsterdam/New York/Oxford. [11] Kovalenkov, A. and M. Wooders (1996) “Epsilon cores of games with limited side payments; Nonemptiness and equal treatment,” Games and Economic Behavior (to appear). [12] Kovalenkov, A. and M. Wooders (1997) “An exact bound on epsilon for non-emptiness of the epsilon-core of an arbitrary game with side payments,” Autonoma University of Barcelona Working Paper 393.97 revised, Mathematics of Operations Research (to appear). [13] Mas-Colell, A. (1984) “On a theorem of Schmeidler,” Journal of Mathematical Economics 13: 206-210. [14] Pascoa, M.(1998) “Nash equilibrium and the law of large numbers,” International Journal of Game Theory 27: 83-92. [15] Pascoa, M. (1993) “Approximate equlibrium in pure strategies for nonatomic games,” Journal of Mathematical Economics 22: 223-241. [16] Rashid, S. (1983) “Equilibrium points of nonatomic games; Asymptotic results,” Economics Letters 12, 7-10. [17] Schmeidler, D. (1973) “Equilibrium points of nonatomic games,” Journal of Statistical Physics 7: 295-300. [18] Wooders, M.H. (1979) “Asymptotic cores and asymptotic balancedness of large replica games” (Stony Brook Working Paper No. 215, Revised July 1980). [19] Wooders, M. (1983) “The epsilon core of a large replica game,” Journal of Mathematical Economics 11, 277-300. [20] Wooders, M. (2001) “Small group negligibility and small group effectiveness; Two sides of the same coin,” University of Warwick, Department of Economics Working Paper (to appear), on-line at http://www.warwick.ac.uk/fac/soc/Economics/wooders/public3.html. [21] Wooders, M. (1994) “Equivalence of games and markets,” Econometrica 62, 1141-1160. [22] Wooders, M. and Zame, W.R. (1984) “Approximate cores of large games,” Econometrica 52, 1327-1350.
URI:	http://wrap.warwick.ac.uk/id/eprint/1589

Request changes to a record

Actions (login required)

View Item