Markov approximations of nonzero-sum differential games

Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki. 2020. Vol. 30. No. 1. P. 3–17.

Averboukh Y.

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.

Keywords: nonzero-sum differential games, approximate Nash equilibria, Markov games, differential inclusion