IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v140y2008i1p314-327.html
   My bibliography  Save this article

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

Author

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

Abstract

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].

Suggested Citation

  • Filipe Martins-da-Rocha, V. & Topuzu, Mihaela, 2008. "Cournot-Nash equilibria in continuum games with non-ordered preferences," Journal of Economic Theory, Elsevier, vol. 140(1), pages 314-327, May.
  • Handle: RePEc:eee:jetheo:v:140:y:2008:i:1:p:314-327
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(07)00076-2
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-585, October.
    4. 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.
    5. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    6. 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.
    7. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-623, September.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    16. 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.
    17. 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.
    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 339-354, October.
    19. 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.
    20. 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.
    21. 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.
    22. Yannelis, Nicholas C., 1987. "Equilibria in noncooperative models of competition," Journal of Economic Theory, Elsevier, vol. 41(1), pages 96-111, February.
    23. 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.
    24. 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.
    25. 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.
    26. Balder, E. J., 1996. "Comments on the existence of equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 307-323.
    27. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barelli, Paulo & Duggan, John, 2015. "Extremal choice equilibrium with applications to large games, stochastic games, & endogenous institutions," Journal of Economic Theory, Elsevier, vol. 155(C), pages 95-130.
    2. Carmona, Guilherme & Podczeck, Konrad, 2014. "Existence of Nash equilibrium in games with a measure space of players and discontinuous payoff functions," Journal of Economic Theory, Elsevier, vol. 152(C), pages 130-178.
    3. Guilherme Carmona, 2016. "Reducible equilibrium properties: comments on recent existence results," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 431-455, March.
    4. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    5. Paulo Barelli & John Duggan, 2011. "Extremal Choice Equilibrium: Existence and Purification with Infinite-Dimensional Externalities," RCER Working Papers 567, University of Rochester - Center for Economic Research (RCER).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:140:y:2008:i:1:p:314-327. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.