Nash Equilibrium under Knightian Uncertainty: A Generalization of the Existence Theorem

Dow and Welang (1994) extended the notion of Nash equilibrium for two-player finite normal games when players are uncertainty on the behavior of his opponents. They showed the existence of equilibrium for any given degree of uncertainty however constant over all possible events, except the null and the whole event). Using a different definition of support, Marinacci (2000) proved the existence of Nash equilibrium for any given uncertainty aversion function. In this paper I will extend Dow and Werlang(1994)’s Nash equilibrium under uncertainty using the same definition of support that they used and a parametrical approach, based on the uncertainty aversion function, which enable me to do comparative static exercises in a easy way. I will work with convex capacities that are “squeezes†of (additive) probability measures, as defined in Coimbra-Lisboa (2003)