Solving the Cournot Oligopoly Game under Incomplete Information with the Possibility of Cooperative Interaction

Abstract

The balance of commodity markets is an extremely important and pressing challenge. There is an active development of research aimed at solving such problem. However, well-known theoretical models do not always adequately reflect the desire of agents to make such individual decisions and search for such compromises to ensure the greatest profit and bring the market to equilibrium.
 The article considers the solution of the Cournot oligopoly game under incomplete information for the case of linear demand and linear costs. The approaches of the reflexive games theory and collective behavior theory are the basis for the construction of the decision-making process by agents. The policy of optimal responses of agents to the expected output volumes of the environment under traditional assumptions about the independence of agents may not lead to equilibrium. Therefore, the article considers and proposes non-traditional solutions that allow agents to cooperate. It is shown that it is enough to jointly regulate the process only at initial stage. After that, it should come to equilibrium if, in the future, agents independently adjust their own output, counting on the maximum expected profit. The necessary assertions and their mathematical proofs are given.