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On Cournot-Nash-Walras equilibria and their computation

Jiri V. Outrata(outrata***at***utia.cas.cz)
Michael C. Ferris(-***at***-.-)
Michal Cervinka(cervinka***at***utia.cas.cz)
Michal Outrata(-***at***-.-)

Abstract: This paper considers a model of Cournot-Nash-Walras (CNW) equilibrium where the Cournot-Nash concept is used to capture equilibrium of an oligopolistic market with non-cooperative players/ rms who share a certain amount of a so-called rare resource needed for their production, and the Walras equilibrium determines the price of that rare resource. We prove the existence of CNW equilibria under reasonable conditions and examine various numerical approaches for their computation. Finally, we demonstrate remarkably stable behavior of CNW equilibria with respect to small perturbations of problem data including, for instance, the available amount of the rare resource.

Keywords: Cournot-Nash-Walras equilibrium, Existence, Stationarity Conditions, Stability, Mathematical Program with Equilibrium Constraints, Implicit programming approach

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation:

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Entry Submitted: 09/29/2015
Entry Accepted: 09/29/2015
Entry Last Modified: 09/29/2015

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