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Some Examples and Counterexamples about Continuity on Equilibrium Problems

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  • Francesco Ciardiello

Abstract

This paper attempts to underline how the Diagonal Transfer Continuity hypothesis (Baye, Tian and Zhou, 1993) and Better-Reply Security (Reny, 1999) are unconnected between themselves as sucient conditions for stating the existence of Nash equilibria. Besides, various examples and counterexamples regarding Nash equilibria existence Theorem (Baye, Tian and Zhou, 1993) and extensions of maximum existence results for bifunctions established for a function of one variable (Baye and and Zhou,1995). We present, also, a sucient conditions for Diagonal Transfer Continuity. Moreover, an example of quasi-concave game having multiple Nash equilibria, in which the aforesaid hypotheses and other improvements (Lignola, 1997) fall, is presented.

Suggested Citation

  • Francesco Ciardiello, 2007. "Some Examples and Counterexamples about Continuity on Equilibrium Problems," Quaderni DSEMS 16-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    • Handle: RePEc:ufg:qdsems:16-2007
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    References listed on IDEAS

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    1. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
    2. M. B. Lignola, 1997. "Ky Fan Inequalities and Nash Equilibrium Points without Semicontinuity and Compactness," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 137-145, July.
    3. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    4. Leo K. Simon, 1987. "Games with Discontinuous Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 569-597.
    5. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    6. Reny, Philip J., 1995. "Local Payoff Security and the Existence of Nash Equilibrium in Discontinuous Games," Working Paper Series 435, Research Institute of Industrial Economics.
    7. Tian, Guoqiang, 1992. "Existence of equilibrium in abstract economies with discontinuous payoffs and non-compact choice spaces," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 379-388.
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    More about this item

    Keywords

    Nash Equilibria Existence; Generalized Convexity; 2 Person Game; Generalized Continuity; Diagonal Transfer Quasi Concavity; Diagonal Transfer Continuity.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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