Open AccessMarkov approximations of nonzero-sum differential games
Author(s) -
Yu.V. Averboukh
Publication year - 2020
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm200101
Subject(s) - markov chain , differential inclusion , nash equilibrium , differential game , mathematics , differential (mechanical device) , ordinary differential equation , outcome (game theory) , markov process , mathematical economics , mathematical optimization , differential equation , computer science , mathematical analysis , physics , statistics , thermodynamics
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.