Pub. online:23 Nov 2020Type:Research ArticleOpen Access
Journal:Informatica
Volume 31, Issue 4 (2020), pp. 769–791
Abstract
In this paper we consider a non-cooperative N players differential game affected by deterministic uncertainties. Sufficient conditions for the existence of a robust feedback Nash equilibrium are presented in a set of min-max forms of Hamilton–Jacobi–Bellman equations. Such conditions are then used to find the robust Nash controls for a linear affine quadratic game affected by a square integrable uncertainty, which is seen as a malicious fictitious player trying to maximize the cost function of each player. The approach allows us to find robust strategies in the solution of a group of coupled Riccati differential equation. The finite, as well as infinite, time horizon cases are solved for this last game. As an illustration of the approach, the problem of the coordination of a two-echelon supply chain with seasonal uncertain fluctuations in demand is developed.
Journal:Informatica
Volume 13, Issue 1 (2002), pp. 73–88
Abstract
Two examples of open-loop differential games are considered in the paper. Starting with simplified dynamic Duel, further it was developed to differential economic Duel modelling problem.
The first example regards a “military” duel of two objects, the second one is about economic duel and presents the economic competition situation. In both cases Monte Carlo models are used. The search for equilibrium is performed by global optimization.
The military model is a convenient illustration of differential game theory. It is interesting for its dynamics, it can be used for teaching purposes. The economic model shows some important features of dynamic competition. In this case objects try to maximize their final profits at the end of the period. The destruction of competitor is a feasible option to achieve this purpose.
New numerical methods and software system for the Internet environment are developed to implement this theory.