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

• Published in: Journal of economic theory Vol. 140; no. 1; pp. 314 - 327
• Main Authors: Filipe Martins-da-Rocha, V., Topuzu, Mihaela
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.05.2008; Elsevier; Elsevier Science Publishing Company, Inc
• Series: Journal of Economic Theory
• Subjects: Continuum games; Economic theory; Equilibrium; Externalities; Externality; Feeble topology; Game theory; Nash equilibrium; Non-ordered preferences; Preferences; Pure Cournot–Nash equilibrium; Studies; Pure Cournot–Nash equilibrium; Non-ordered preferences; Feeble topology; Continuum games; C72
• ISSN: 0022-0531; 1095-7235
• DOI: 10.1016/j.jet.2007.05.002

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].