Group for Research in Decision Analysis

# Differential Games with Random Time Horizon

## Ekaterina Shevkoplyas – Saint Petersburg State University, Russia

The class of differential games with random time horizon is considered. For such a formulation of the game the expected integral payoff of the player can be represented in the form of double integral which is not suitable for standard methods of dynamic programming. The propositions about reduction of the problem to standard form are established. Also the Hamilton-Jacobi-Bellman equation is derived. The cooperative form of the game is considered and a problem of the time-consistent Shapley Value construction is examined. An application of the theoretical results are illustrated with a model of non-renewable resource extraction by $$n$$ firms or countries.