Abstract

The relevance of this article is due to the insufficient development of the oligopoly model. In the study of conflict-controlled processes with arbitrary duration, attention to oligopoly models remains limited. Differential games for two participants simulating the joint development of a non-renewable resource are considered. A situation is described in which each player has an individual moment of exit from the game, specified by a random variable with a known distribution function. At the moment of completion of the first stage of the game, the remaining player receives the final payment. It is assumed that he continues to work on the resource. The final payment can be set equal to the optimal income of the player, which is determined by solving the corresponding optimal control problem.This paper analyzes a differential game of joint development of a non-renewable resource, establishes the structure of its expected payoff, and formally derives the Hamilton-Jacobi-Bellman equation for the game under consideration

Keywords

models, differential games, oligopoly, development, resource, income, equation, problem

References

  1. Petrosyan, L.A., & Shevkoplyas, E.V. (2000). Cooperative differential games with random duration. Bulletin of St. Petersburg University. Series 1: Mathematics, Mechanics, Astronomy, 4, 18-23.

  2. Petrosyan, L.A., & Murzov, N.V. (1966). Game-theoretic problems in mechanics. Lithuanian Mathematical Journal, 6(3), 423-433.

  3. Kostyunin, S.Yu., & Shevkoplyas, E.V. (2011). On simplification of integral payoff in differential games with random duration. Bulletin of St. Petersburg University. Series 10: Applied Mathematics, Informatics, Control Processes, 4, 47-56.

  4. Shevkoplyas, E.V. (2009). Hamilton-Jacobi-Bellman equation in differential games with random duration. Mathematical Game Theory and Applications, 1(2), 98-118.

  5. Saparova, G.B., & Sultan, K.N. (2021). Mathematical models for financial risk assessment. Bulletin of Osh Technological University, 1, 142-145.

Suggested citation

Saparova, G., & Azhieva, E. (2025). ABOUT ONE METHOD OF DIFFERENTIAL GAMES IN THE RESOURCE MANAGEMENT PROBLEM. News of Osh Technological University, 25(1), 156-160.