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Cournot-Nash equilibria in continuum games with non-ordered preferences

  • Filipe Martins-da-Rocha, V.
  • Topuzu, Mihaela

In the usual framework of continuum games with externalities, we substantially generalize Cournot-Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79-94; On the existence of Cournot-Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207-223; A unifying pair of Cournot-Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437-470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237-246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9-15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345-348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the "new" existence theorems, J. Math. Econ. 3 (1976) 313-316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233-245].

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 140 (2008)
Issue (Month): 1 (May)
Pages: 314-327

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Handle: RePEc:eee:jetheo:v:140:y:2008:i:1:p:314-327
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
  2. Noguchi, Mitsunori, 2000. "Economies with a measure space of agents and a separable commodity space," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 157-173, September.
  3. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
  4. Kim, Taesung & Yannelis, Nicholas C., 1997. "Existence of Equilibrium in Bayesian Games with Infinitely Many Players," Journal of Economic Theory, Elsevier, vol. 77(2), pages 330-353, December.
  5. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
  6. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
  7. 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 427-33, July.
  8. Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 237-246, December.
  9. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-23, September.
  10. Yannelis, Nicholas C., 1987. "Equilibria in noncooperative models of competition," Journal of Economic Theory, Elsevier, vol. 41(1), pages 96-111, February.
  11. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-85, October.
  12. V. Martins-da-Rocha, 2004. "Equilibria in large economies with differentiated commodities and non-ordered preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 529-552, March.
  13. Filipe Martins-da-Rocha, V., 2003. "Equilibria in large economies with a separable Banach commodity space and non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 863-889, November.
  14. Ali Khan, M. & Rustichini, Aldo, 1993. "Cournot-Nash equilibrium distributions of games with uncertainty and imperfect information," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 35-59.
  15. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
  16. Balder, Erik J, 1995. "A Unifying Approach to Existence of Nash Equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 79-94.
  17. Balder, E. J., 1996. "Comments on the existence of equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 307-323.
  18. Balder, Erik J, 1991. "On Cournot-Nash Equilibrium Distributions for Games with Differential Information and Discontinuous Payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 339-54, October.
  19. Balder, Erik J., 1999. "On the existence of Cournot-Nash equilibria in continuum games," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 207-223, October.
  20. Balder, Erik J., 2000. "Incompatibility of Usual Conditions for Equilibrium Existence in Continuum Economies without Ordered Preferences," Journal of Economic Theory, Elsevier, vol. 93(1), pages 110-117, July.
  21. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  22. Borglin, Anders & Keiding, Hans, 1976. "Existence of equilibrium actions and of equilibrium : A note on the `new' existence theorems," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 313-316, December.
  23. Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, vol. 102(2), pages 437-470, February.
  24. Rath, Kali P., 1996. "Existence and upper hemicontinuity of equilibrium distributions of anonymous games with discontinuous payoffs," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 305-324.
  25. Khan, M. Ali & Vohra, Rajiv, 1984. "Equilibrium in abstract economies without ordered preferences and with a measure space of agents," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 133-142, October.
  26. Noguchi, Mitsunori, 1997. "Economies with a continuum of agents with the commodity-price pairing (l[infin], l1)," Journal of Mathematical Economics, Elsevier, vol. 28(3), pages 265-287, October.
  27. Noguchi, Mitsunori, 1997. "Economies with a continuum of consumers, a continuum of suppliers and an infinite dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 1-21, February.
  28. Cornet, Bernard & Topuzu, Mihaela & Yildiz, Aysegul, 2003. "Equilibrium theory with a measure space of possibly satiated consumers," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 175-196, June.
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