Two approaches to dynamic capacity expansion problem in oligopoly

The productive capacity is determinant of a company’s success once it allows meeting the current and future demand. This article proposes quantitative models for determining investments in the development of the productive capacity in competitive oligopolistic markets, based on the Nash Equilibrium, formulated as an optimization problem. Two types of markets are considered: the market with elastic demand (Cournot market) and the market with inelastic demand. The second type of market is characteristic of commodity markets (oil, gas, metallurgical coal, etc.), which are located at the beginning of the production chain for the final product creation. In the first case, the problem is formulated as a set of interrelated quadratic optimization problems. To solve this problem, a method of converting the original problem to the mixed complementarity problem (MCP) is proposed. In the second case, methods based on multi-agent simulation and matrix games analyses are proposed. A simulation model of the company (agent) has been developed, which models the mutual influence of agents investment and market dynamics. The proposed method allows obtaining an approximate solution of the original problem, since the heuristic principles and algorithms of the behavior of agents are used in the construction of the model.