This paper examines the problem of choice investment strategies of firms in an oligopoly market. We study the impact of investment strategies of companies on their financial performance and the efficiency of investment under demand uncertainty. A mathematical model for choosing investments in the development of production capacities of companies in competitive oligopolistic markets based on the Nash equilibrium presented, formulated as an optimization problem. Two types of market are considered: a market with elastic demand (Cournot market) and a market with inelastic demand. In the first case, the problem is formulated as a set of interrelated problems of quadratic optimization. To solve this problem, a method of converting the original problem to solving the mixed complementarity problem (MCP) is proposed. In the second case, a method for solving the problem is proposed, based on the joint use of multi-agent modeling and analysis of matrix games. A simulation model was developed that takes into account the relationship between the investments of companies (agents) and market dynamics. A solution of the problem reduced to the analysis of the dynamic bimatrix game, wherein the payoff matrix formed by numerical simulation.