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Anonymity in Nonatomic Games

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  • Lorenzo Rocco

    (Department of Economics, University of Milan-Bicocca)

Abstract

In nonatomic games, anonymity must be assumed in order to prove the existence of a Nash equilibrium in pure strategies. This can be formalized by making payoffs dependent either on the players' distribution on the action set or on the strategy mean. An extension of Rath's (1992) proof to the case of limited anonymity is proposed: the behavior of the population as a whole, is shown sufficient to get equilibrium existence in pure strategies.

Suggested Citation

  • Lorenzo Rocco, 2002. "Anonymity in Nonatomic Games," Working Papers 53, University of Milano-Bicocca, Department of Economics, revised Aug 2002.
  • Handle: RePEc:mib:wpaper:53
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    References listed on IDEAS

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    1. Dubey, Pradeep & Kaneko, Mamoru, 1985. "Information patterns and Nash equilibria in extensive games -- II," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 247-262, December.
    2. Karni, Edi & Levin, Dan, 1994. "Social Attributes and Strategic Equilibrium: A Restaurant Pricing Game," Journal of Political Economy, University of Chicago Press, vol. 102(4), pages 822-840, August.
    3. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    4. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
    5. Constantinides, George M. & Rosenthal, Robert W., 1984. "Strategic analysis of the competitive exercise of certain financial options," Journal of Economic Theory, Elsevier, vol. 32(1), pages 128-138, February.
    6. Masso, Jordi, 1993. "Undiscounted equilibrium payoffs of repeated games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 243-264.
    7. Masso, Jordi & Rosenthal, Robert W., 1989. "More on the "anti-folk theorem"," Journal of Mathematical Economics, Elsevier, vol. 18(3), pages 281-290, June.
    8. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808, Elsevier.
    9. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    10. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
    11. Pascoa Mario Rui, 1993. "Noncooperative Equilibrium and Chamberlinian Monopolistic Competition," Journal of Economic Theory, Elsevier, vol. 60(2), pages 335-353, August.
    12. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 427-433, July.
    13. D'Agata, Antonio, 2005. "Star-shapedness of Richter-Aumann integral on a measure space with atoms: theory and economic applications," Journal of Economic Theory, Elsevier, vol. 120(1), pages 108-128, January.
    14. Dubey, Pradeep & Shapley, Lloyd S., 1994. "Noncooperative general exchange with a continuum of traders: Two models," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 253-293, May.
    15. Kaneko, Mamoru, 1982. "Some remarks on the folk theorem in game theory," Mathematical Social Sciences, Elsevier, vol. 3(3), pages 281-290, October.
    16. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April.
    17. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    18. Sabourian, Hamid, 1990. "Anonymous repeated games with a large number of players and random outcomes," Journal of Economic Theory, Elsevier, vol. 51(1), pages 92-110, June.
    19. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
    20. Aumann, Robert J., 1976. "An elementary proof that integration preserves uppersemicontinuity," Journal of Mathematical Economics, Elsevier, vol. 3(1), pages 15-18, March.
    21. Giulio Codognato & Sayantan Ghosal, 2003. "On existence of undominated pure strategy Nash equilibria in anonymous nonatomic games: a generalization," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(4), pages 493-498, September.
    22. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January.
    23. Rafael Rob, 1987. "Entry, Fixed Costs and the Aggregation of Private Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 619-630.
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