Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-Quasiconcave Payoffs

Michael R. Baye, Guoqiang Tian and Jianxin Zhou
The Review of Economic Studies
Vol. 60, No. 4 (Oct., 1993), pp. 935-948
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/2298107
Page Count: 14
  • Download ($42.00)
  • Subscribe ($19.50)
  • Cite this Item
Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-Quasiconcave Payoffs
Preview not available

Abstract

This paper characterizes pure-strategy and dominant-strategy Nash equilibrium in non-cooperative games which may have discontinuous and/or non-quasiconcave payoffs. Conditions called diagonal transfer quasiconcavity and uniform transfer quasiconcavity are shown to be necessary and, with conditions called diagonal transfer continuity and transfer upper semicontinuity, sufficient for the existence of pure-strategy and dominant-strategy Nash equilibrium, respectively. The results are used to examine the existence or non-existence of equilibrium in some well-known economic games with discontinuous and/or non-quasiconcave payoffs. For example, we show that the failure of the existence of a pure-strategy Nash equilibrium in the Hotelling model is due to the failure of an aggregator function to be diagonal transfer quasiconcave-not the failure of payoffs to be quasiconcave, as has been elsewhere conjectured.

Page Thumbnails

  • Thumbnail: Page 
935
    935
  • Thumbnail: Page 
936
    936
  • Thumbnail: Page 
937
    937
  • Thumbnail: Page 
938
    938
  • Thumbnail: Page 
939
    939
  • Thumbnail: Page 
940
    940
  • Thumbnail: Page 
941
    941
  • Thumbnail: Page 
942
    942
  • Thumbnail: Page 
943
    943
  • Thumbnail: Page 
944
    944
  • Thumbnail: Page 
945
    945
  • Thumbnail: Page 
946
    946
  • Thumbnail: Page 
947
    947
  • Thumbnail: Page 
948
    948