Abstract:
The paper is concerned with approximate solutions of nonzero-sum differential games.
An approximate Nash equilibrium can be designed by a given solution of an auxiliary continuous-time dynamic game.
We consider the case when dynamics is determined by a Markov chain.
For this game the value function is determined by an ordinary differential inclusion.
Thus, we obtain a construction of approximate equilibria with the players' outcome close to the solution of the differential inclusion.
Additionally, we propose a way of designing a continuous-time Markov game approximating the original dynamics.