Singularly Perturbed Piecewise Deterministic Games

Abstract. In this paper we consider a class of hybrid stochastic games with the piecewise openloop information structure. These games are indexed over a parameter which represents the time scale ratio between the stochastic (jump process) and the deterministic (differential state equation) parts of the dynamical system. We study the limit behavior of Nash equilibrium solutions to the hybrid stochastic games when the time scale ratio tends to 0. We also establish that an approximate equilibrium can be obtained for the hybrid stochastic games using a Nash equilibrium solution of a reduced order sequential discrete state stochastic game and a family of local deterministic infinite horizon open-loop differential games defined in the stretched out time scale. A numerical illustration of this approximation scheme is also developed. Key words. n-person games, noncooperative games, stochastic games, differential games, time scale analysis, singular perturbations AMS subject classifications. 9...

• Type: Journal
• Year: 2008
• Where: SIAMCO
• Authors: Alain Haurie, Francesco Moresino
• Keywords: Hybrid Stochastic Games, SIAMCO 2008, Stochastic Games, Time Scale