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Some Examples and Counterexamples about Continuity on Equilibrium Problems

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Author Info
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.

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Paper provided by Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia in its series Quaderni DSEMS with number 16-2007.

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Date of creation: Jul 2007
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Handle: RePEc:ufg:qdsems:16-2007

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Related research
Keywords: Nash Equilibria Existence; Generalized Convexity; 2 Person Game; Generalized Continuity; Diagonal Transfer Quasi Concavity; Diagonal Transfer Continuity.;

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium

This paper has been announced in the following NEP Reports:

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  1. 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.
  2. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Blackwell Publishing, vol. 54(4), pages 569-97, October. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Blackwell Publishing, vol. 60(4), pages 935-48, October. [Downloadable!] (restricted)
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