Вероятностная модель дуополии

Abstract

A probabilistic model of the duopoly market is constructed. The model is based on the assumption of the random nature of economic variables that determine the market behavior of consumers and competing firms: purchasing power; total costs associated with the production and sale of a unit of goods; commodity prices set by firms. Within the framework of the constructed model, expected values of the profit received and the amount of goods sold were found in the form of functionals of the probability density functions of purchasing power, costs, and prices for goods. Several special cases are considered when the laws of distribution of purchasing power, costs and prices are either exponential or degenerate. In each case numerical modeling was carried out, types of duopolistic relationships between the firms leading to Cournot and Bertrand market equilibria were determined, and economic criteria for the stability 
 of these duopoly market equilibria were established. It is shown that if all random variables included in the probabilistic model have exponential distribution laws, then in the duopoly market may arise an equilibrium state that is different from the Cournot equilibrium and the Bertrand equilibrium.