Sufficient conditions for Nash equilibria inN-person games over reflexive Banach spaces

  • R. J. Williams
Contributed Papers


Sufficient conditions are obtained for the existence of Nash equilibrium points inN-person games when the strategy sets are closed, convex subsets of reflexive Banach spaces. These conditions require that each player's cost functional is convex in that player's strategy, weakly continuous in the strategies of the other players, weakly lower semicontinuous in all strategies, and furthermore satisfies a coercivity condition if any of the strategy sets is unbounded. The result is applied to a class of linear-quadratic differential games with no information, to prove that equilibrium points exist when the duration of these games is sufficiently small.

Key Words

N-person games Nash equilibrium reflexive Banach spaces linear-quadratic differential games 


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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • R. J. Williams
    • 1
  1. 1.Department of MathematicsStanford UniversityStanford

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