Variational preferences and equilibria in games under ambiguous belief correspondences

• This paper studies strategic games under ambiguous belief correspondences in case of variational preferences.
• An existence theorem is given for the corresponding equilibrium concept.
• Examples show the model applicability.
• The study of the limit behavior of equilibria under perturbations on the parameters of ambiguity concludes the paper.

Variational preferences have been introduced to study the robustness of macroeconomic models with respect to ambiguity. The Decision Theory literature has shown that this family of preferences provides a tractable and flexible tool in order to deal with this kind of uncertainty in general settings. In fact, variational preferences are equipped with an accurate and explicit parametrization of the decision maker's attitude towards ambiguity, which is indeed represented by a cost function of the probabilities (called index of ambiguity aversion). In the present work, we study the effect of variational preferences in strategic form games under ambiguity in which players' uncertainty is expressed entirely in the space of lotteries over consequences by belief correspondences of the strategy profile chosen by the agents. We focus on primary theoretical issues related to this model that constitute a required background for applications or numerical methods. First, we give a general equilibrium existence result that we apply to a particular model in which belief correspondences depend on the equilibria of specific subgames. Other numerical examples are presented to show the model applicability. Finally, we look at the consequences of parameter changes on equilibrium predictions and study the limit behavior of equilibria under perturbations on the index of ambiguity aversion and belief correspondences. All the results are sufficiently general to be a useful tool in any interdisciplinary problem in which strategic interaction is affected by ambiguity.