Nash equilibria for games in capacities

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, 1999, 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.