Location Invariance and Games with Ambiguity

This paper proposes that the ambiguity reflected by a set of priors remains unchanged when the set is translated within the probability simplex, i.e. ambiguity is location invariant. This unifies and generalises numerous influential definitions of ambiguity in the literature. Location invariance is applied to normal form games where players perceive strategic ambiguity. The set of translations of a given set of priors is shown to be isomorphic to the probability simplex. Thus considering mixtures of translations has a convexifying effect similar to considering mixed strategies in the absence of ambiguity. This leads to the proof of equilibrium existence in complete generality using a fixed point theorem. We illustrate the modelling capabilities of our solution concept and demonstrate how our model can intuitively describe strategic interaction under ambiguity.