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Continuity of the payoff functions

Author

Listed:
  • Allan Muir

    (Department of Mathematics, City University, Northampton Square, London EC1V 0HB, UK)

  • Dionysius Glycopantis

    (Department of Economics, City University, Northampton Square, London EC1V 0HB, UK)

Abstract

In his Nash equilibrium paper, Glicksberg states that the payoff functions are continuous. Such a function is defined on the product of mixed strategies, which are the Borel probability measures on a compactum, endowed with the product of the weak topologies. The continuity property is used in proving the existence of Nash equilibria. This note proves that the payoff functions are continuous, which is not immediate to establish.

Suggested Citation

  • Allan Muir & Dionysius Glycopantis, 2000. "Continuity of the payoff functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 239-244.
    • Handle: RePEc:spr:joecth:v:16:y:2000:i:1:p:239-244
    Note: Received: June 10, 1999; revised version: June 24, 1999
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    Citations

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    Cited by:

    1. N. Sofronidis, 2008. "Topological upper limits of mixed Nash equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(2), pages 395-399, February.
    2. Aliprantis, Charalambos D. & Glycopantis, Dionysius & Puzzello, Daniela, 2006. "The joint continuity of the expected payoff functions," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 121-130, April.

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