Annals of Operations Research

, Volume 248, Issue 1–2, pp 345–363

# Endogenous interval games in oligopolies and the cores

Original Paper

## Abstract

In this article we study interval games in oligopolies following the $$\gamma$$-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 $$\gamma$$-cores. The first condition permits to ascertain that even for linear and symmetric industries the interval $$\gamma$$-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 $$\gamma$$-core is non-empty, under natural properties of profit and cost functions.

## Keywords

Interval game Oligopoly $$\gamma$$-Cores Hurwicz criterion  Quadratic Bézier curve

C71 D43

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