Geodesic
Markov approximations of nonzero-sum differential games
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 1, pp. 3-17

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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. 
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     title = {Markov approximations of nonzero-sum differential games},
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Yu. V. Averboukh. Markov approximations of nonzero-sum differential games. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/VUU_2020_30_1_a0/