Search for dynamic equilibrium in duel problems by global optimization

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.