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On Cournot-Nash Equilibrium Distributions for Games with Differential Information and Discontinuous Payoffs

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  • Balder, Erik J

Abstract

Mas-Colell's model for equilibrium distributions in "large" anonymous games is extended by the introduction of an abstract, non-topological notion of players' characteristics. The generality of this model allows us to include as a component of a player's characteristic her/his degree of well-informedness (differential information). This makes it possible to address a generalization of a model recently formulated by Khan-Rustichini. We show that one can remove their rather unnatural compactness condition on the space of admissible decision rules, provided that one allows for decision rules which are randomized. Our utility functions need not be continuous; this particular technical aspect solves an open question of Khan concerning Mas-Colell's original model. Our method of proof is based on the novel observation that Cournot-Nash equilibrium distributions are precisely the solutions of a variational inequality for transition probabilities.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:1:y:1991:i:4:p:339-54
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    Cited by:

    1. Cetemen, Doruk & Feng, Felix Zhiyu & Urgun, Can, 2023. "Renegotiation and dynamic inconsistency: Contracting with non-exponential discounting," Journal of Economic Theory, Elsevier, vol. 208(C).
    2. Héctor Jasso-Fuentes & Tomás Prieto-Rumeau, 2024. "Constrained Markov Decision Processes with Non-constant Discount Factor," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 897-931, August.
    3. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    4. 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.
    5. Doruk Cetemen & Felix Zhiyu Feng & Can Urgun, 2019. "Contracting with Non-Exponential Discounting: Moral Hazard and Dynamic Inconsistency," Working Papers 2019-17, Princeton University. Economics Department..
    6. Balder, Erik J., 2004. "An equilibrium existence result for games with incomplete information and indeterminate outcomes," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 297-320, June.
    7. 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.
    8. Balder, E. J., 1996. "Comments on the existence of equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 307-323.
    9. Yang, Jian, 2022. "A Bayesian nonatomic game and its applicability to finite-player situations," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    10. 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.
    11. 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.

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