International Review of Economics

, Volume 54, Issue 2, pp 225–247 | Cite as

Anonymity in nonatomic games

  • Lorenzo RoccoEmail author


This paper purpose is twofold. First, it offers a critical review of the proofs of existence of pure strategy Nash Equilibria in nonatomic games. In particular, it focuses on the alternative ways of formalizing the critical assumption of anonymity. Second, the paper proves the existence of pure strategy Nash Equilibria by relaxing anonymity and allowing instead for “limited anonymity” (i.e. players’ decisions depend on the average strategy of a finite number of players’ subsets and not on the average strategy of the whole set of players). (JEL: C72, C79)


nonatomic games Nash equilibrium anonymity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aliprantis C.D. and Burkinshaw O., Principles of Real Analysis, 3rd. ed., London: Academic Press, 1998.Google Scholar
  2. Aumann R.J., (1964) “Markets with a Continuum of Traders”. Econometrica 32: 39–50CrossRefGoogle Scholar
  3. Aumann R.J., (1965)“Integrals of Set-Valued Functions”. Journal of Mathematical Analysis Applications 12: 1–12CrossRefGoogle Scholar
  4. Aumann R.J.,(1966) “Existence of a Competitive Equilibrium in Markets with a Continuum of Traders”. Econometrica 34: 1–17CrossRefGoogle Scholar
  5. Aumann R.J., (1976) “An Elementary Proof That Integration Preserves Uppersemicontinuity”. Journal of Mathematical Economics 3: 15–18CrossRefGoogle Scholar
  6. Berge C., (1962) Espaces Topologiques, Fonctions Multivoques. Paris, Dunod.Google Scholar
  7. Codognato G., Ghosal S., (2003) “On Existence of Undominated Pure Strategy Nash Equilibria in Anonymous Nonatomic Games: A Generalization”,International Journal of Game Theory31(4): 493–98.Google Scholar
  8. Constantinides G.M. and Rosenthal R.W., “Strategic Analysis of the Competitive Exercise of Certain Financial Options”, Journal of Economic Theory, 1984, 32, pp. 128–38.Google Scholar
  9. D’Agata A., “Star-Shapedness of Richter-Aumann Integral on a Measure Space with Atoms: Theory and Economic Applications”,Journal of Economic Theory,2005, 120 (1), pp. 108–28.Google Scholar
  10. Dubey P. and Kaneko M., “Information Patterns and Nash Equilibria in Extensive Games”,Mathematical Social Sciences,1984, 8, pp. 111–39.Google Scholar
  11. Dubey P. and Shapley L.S., “Noncooperative General Exchange with a Continuum of Traders: Two Models”, Journal of Mathematical Economics,1994, 23, pp. 25393.Google Scholar
  12. Green E.J., “Noncooperative Price Taking in Large Dynamic Markets”, Journal of Economic Theory,1980, 22 (2), pp. 155–81.Google Scholar
  13. Kaneko M., “Some Remarks on the Folk Theorem in Game Theory”, Matematical Social Sciences,1982, 3, pp. 281–90.Google Scholar
  14. Karni E. and Levine D., “Social Attributes and Strategic Equilibrium: A Restaurant Pricing Game”,Journal of Political Economy,1994, 102 (4), pp. 822–40.Google Scholar
  15. Karni E. and Schmeidler D., “Fixed Preferences and Changing Tastes”, American Economic Review,1990, 80(2), pp. 262–67.Google Scholar
  16. Khan A.M., Rath K.P.,and Sun Y., “On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players”, Journal of Economic Theory,1997, 76, pp. 13–46.Google Scholar
  17. Khan A.M., and Sun Y., “On Large Games with Finite Actions: A Synthetic Treatment”, in T. Maruyama and W. Takahashi, eds., Nonlinear and Convex Analysis in Economic Theory,Berlin: Springer-Verlag, 1994.Google Scholar
  18. Khan A.M., and Sun Y., “Pure Strategies in Games with Private Information”, Journal of Mathematical Economics,1995, 24, pp. 633–53.Google Scholar
  19. Khan A.M., and Sun Y., “Non Cooperative Games with Many Players”, in R. Aumann and S. Hart, eds., Handbook of Game Theory with Economic Applications, Amsterdam: North Holland, 2002, Vol. 3, Chap. 46, pp. 1761–1808.Google Scholar
  20. Konishi H., Le Breton M.,and Weber S. (1997a), “Equilibria in a Model with Partial Rivalry”, Journal of Economic Theory, 1997, 72, pp. 225–37.Google Scholar
  21. Konishi H., Le Breton M.,and Weber S. (1997b), “Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities”, Games and Economic Behavior,1997, 21, pp. 161–82.Google Scholar
  22. Mas-Colell A., “On a Theorem of Schmeidler”, Journal of Mathematical Economics, 1984, 13, pp. 201–6.Google Scholar
  23. Masso’ J., “Undiscounted Equilibrium Payoffs of Repeated Games with a Continuum of Players”, Journal of Mathematical Economics,1993, 22, pp. 243–64.Google Scholar
  24. Masso’ J., and Rosenthal R.W., “More on the ‘Anti-Folk Theorem’ ” , Journal of Mathematical Economics,1989, 18, pp. 281–90.Google Scholar
  25. May K.O., “A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decisions”, Econometrica,1952, 20, pp. 640–84.Google Scholar
  26. Milgrom P.R. and Weber R.J., “Distributional Strategies for Games with Incomplete Information”, Mathematics of Operations Research,1985, 10, pp. 619–32.Google Scholar
  27. Pascoa M.R., “Noncooperative Equilibrium and Chamberlinian Monopolistic Competition”, Journal of Economic Theory,1993, 60, pp. 335–53.Google Scholar
  28. Rath K.P., “A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players”, Economic Theory, 1992, 2, pp. 427–33.Google Scholar
  29. Rob R., “Entry, Fixed Costs and the Aggregation of Private Information”, Review of Economic Studies,1987, LIV, pp. 619–30.Google Scholar
  30. Sabourian H., “Anonymous Repeated Games with a Large Number of Players and Random Outcomes”, Journal of Economic Theory,1990, 51(1), pp. 92–110.Google Scholar
  31. Schmeidler D., “Equilibrium Points of Nonatomic Games”, Journal of Statistical Physics,1973, 34(4), pp. 295–300.Google Scholar
  32. Shapley L.S. and Shubik M., “Trade Using One Commodity as a Means of Payment”, Journal of Political Economy,1977, 85(5), pp. 937–68.Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of PaduaPaduaItaly

Personalised recommendations