Oligopoly Model with Interdependent Preferences : Existence and Uniqueness of Nash Equilibrium

We propose a model to describe and study the effect of social interdependent preferences in a Cournot oligopoly based on a game in which the utility functions of firms depend on a combination of weighted profits of their competitors. If social interaction is neglected, the model reduces to the classic Cournot game, diverting from it as the role of social interaction becomes more and more relevant. Several synthetic measures are proposed to summarize the overall behavior of the agents and some configurations characterized by particular interactional structures are presented. Finally, the study of the well-posedness of the proposed framework is investigated, in terms of the existence and uniqueness of Nash equilibria. To this end, we generalize the conditions under which the existence and/or uniqueness of Nash equilibrium in classic games is guaranteed for particular Cournotian oligopoly models without interdependent preferences. In particular, we focus on two families of oligopolies, respectively consisting of “concave” oligopolies and oligopolies with isoelastic demand function