# Endogenous interval games in oligopolies and the cores

Aymeric Lardon ()
Aymeric Lardon: University of Nice-Sophia Antipolis

Annals of Operations Research, 2017, vol. 248, issue 1, 345-363

Abstract: Abstract 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.

Keywords: Interval game; Oligopoly; $$\gamma$$ γ -Cores; Hurwicz criterion; Quadratic Bézier curve (search for similar items in EconPapers)
JEL-codes: C71 D43 (search for similar items in EconPapers)
Date: 2017
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