Economic Theory

, Volume 35, Issue 2, pp 321–331 | Cite as

Nash equilibria for games in capacities

Research Article

Abstract

This paper provides a formal generalization of Nash equilibrium for games under Knightian uncertainty. The paper is devoted to counterparts of the results of Glycopantis and Muir (Econ Theory 13:743–751, l999, Econ Theory 16:239–244, 2000) for capacities. We prove that the expected payoff defined as the integral of a payoff function with respect to the tensor product of capacities on compact Hausdorff spaces of pure strategies is continuous if so is the payoff function. We prove also an approximation theorem for Nash equilibria when the expected utility payoff functions are defined on the space of capacities.

Keywords

Knightian uncertainty Nash equilibrium Capacities 

JEL Classification Numbers

C72 D81 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.WFRI, Warwick Business SchoolThe University of WarwickCoventryUK
  2. 2.Department of Mechanics and MathematicsLviv National UniversityLvivUkraine
  3. 3.Institute of MathematicsUniversity of RzeszówRzeszówPoland

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