Annals of Operations Research

, Volume 248, Issue 1–2, pp 345–363 | Cite as

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 

JEL Classification

C71 D43 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.GREDEG UMR 7321 CNRSUniversity of Nice-Sophia AntipolisValbonneFrance

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