Game-theoretic modelling of a corporation’s optimal capital structure based on Nash bargaining solution
Egor M. Bogatov, Cand. Sc. (Physics and Mathematics), Associate Prof. of Mining Dept.
Gubkin Branch of the National University of Science and Technology “MISIS”; Associate Prof. of Further Mathematics and Informatics Dept. Stary Oskol Technological Institute named after A. A. Ugarov – Branch of the National University of Science and Technology “MISIS”
Elena G. Demidova, Cand. Sc. (Econ.), Associate Prof. of Economics, Management and
Production Organisation Dept. Stary Oskol Technological Institute named after A. A. Ugarov
– Branch of the National University of Science and Technology “MISIS”
Abstract
The article deals with constructing a game-theoretic model of capital structure that would take into account the interests of the company’s owners (player 1) and its managers (player 2) to the maximum extent possible, as well as testing this model. Methodologically, the research rests on Nash bargaining solution for two-person cooperative games, where the elements of player 1’s payoff matrix A are the return on equity of enterprises, and the elements of player 2’s payoff matrix B are inversely proportional to the weighted average cost of capital (WACC) (in this setting, the task of finding a balanced capital structure is completely new). As a result, the game-theoretic algorithm for determining the Pareto optimal value of ROE and the corresponding share of borrowed capital has been tested on the data from five leading companies in the Russian metallurgical sector observed during 2019–2023. In this case, we identify the elements of player 1’s payment matrix A using the DuPont five-factor model, and calculate WACC in two ways (based on dividends and based on the average market value of equity capital). The Pareto optimal value of ROE in the first and second cases differs significantly (83% and 121%). This indicates that the second method of calculating WACC is not very acceptable in Nash bargaining solution. In the first case, we have calculated the optimal share of borrowed capital Kd o by mixing the shares Kd 1, Kd 2 for two pure strategies with weights of 0.94 and 0.06 respectively. As a result, the desired value of borrowed capital is approximately 51%. The conclusions of the simulation game-theoretic modelling according to the presented scheme can be used as a basis for making financial and economic decisions that limit the use of borrowed capital. In addition, the ROE value calculated in the process of solving the arbitration scheme can be used as a scientifically based target value for this indicator when forecasting the capital structure.
Keywords: capital structure; ROE; WACC; game-theoretic modelling; two-person cooperative game; Nash bargaining solution; Pareto optimal solution.
For citation: Bogatov E. M., Demidova E. G. Game-theoretic modelling of a corporation’s optimal capital structure based on Nash bargaining solution. Digital Models and Solutions. 2026. Vol. 5, no. 1, pp. 53–76. DOI: 10.29141/2949-477X-2026-5-1-4. EDN: KBUFPJ.
