Numerical solutions to differential games based on approximations by Markov games

The dynamic programming equation arising in zero-sum differential games can be approximated by a sequence of finite-state Markov games that can be efficiently solved by a version of the modified policy iteration method. The authors use the approach to solve a combat problem related to the classical two-car game of R. Isaacs (Differential Games, Wiley, 1965). The results of this computational experiment indicate that the approach could be an effective tool for the solution of a variety of more complex models of conflict