Ambiguous games without a state space and full rationality

Abstract

This work aims to differentiate and to better understand the assumptions that must be imposed on the structure of ambiguity and on the attitudes towards ambiguity in order to have existence of equilibria in games under ambiguous belief correspondences. In the present paper, this class of games is studied under substantially weaker assumptions on agents' preferences, as they are not required to be rational and therefore do not have any functional representation. A new approach is required to deal with preferences that are not rational, in this particular framework; in fact, the present work shows that the attitudes of agents towards the imprecision of probabilistic beliefs play a key role in the issue of equilibrium existence, whenever they are combined with some property of convexity/concavity of the ambiguous belief correspondences. The paper also studies the role played by these assumptions in different specific models, (such as incomplete information games with multiple priors or games under strategic ambiguity), so as to illustrate the applicability of the results of equilibrium existence and connections with previous literature.