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Siberian Journal of Numerical Mathematics

2015 year, number 4

Oligopolistic interacting markets

Valery Ivanovich Zorkaltsev, Marina Alexandrovna Kiseleva
Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Lermontov St., 130, Irkutsk, 664033, Russia
Keywords: модель Курно, равновесие Нэша, потенциальная игра, Cournot model, Nash equilibria, potential game

Abstract

The model of several interacting Cournot markets is considered. The markets are named interacting because the same number of producers act on each of them. Every producer chooses his own supply volumes on every market using the price situations, his own costs and production and delivery limitations. It is proved that in the case of the linear demand functions the problem of finding the Nash equilibria in the interacting Cournot markets model represents a potential game, i. e. it is equivalent to a mathematical programming problem. Nonlinear demand functions linearization procedures and preferences of initial problem reduction to the potential game are discussed.