Endogenous interval games in oligopolies and the cores

In this article we study interval games in oligopolies following the $$\gamma $$ γ -approach. First, we analyze their non-cooperative foundation and show that each coalition is associated with an endogenous real interval. Second, the Hurwicz criterion turns out to be a key concept to provide a necessary and sufficient condition for the non-emptiness of each of the induced core solution concepts: the interval and the standard $$\gamma $$ γ -cores. The first condition permits to ascertain that even for linear and symmetric industries the interval $$\gamma $$ γ -core is empty. Moreover, by means of the approximation technique of quadratic Bézier curves we prove that the second condition always holds, hence the standard $$\gamma $$ γ -core is non-empty, under natural properties of profit and cost functions.