Singularly perturbed piecewise deterministic games

In this paper we consider a class of hybrid stochastic games with the piecewise open-loop information structure. These games are indexed over a parameter $\varepsilon$ 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.


Published in:
Siam Journal on Control and Optimization, 47, 1, 73-91
Year:
2008
Publisher:
Society for Industrial and Applied Mathematics
ISSN:
0363-0129
Keywords:
Laboratories:




 Record created 2010-07-22, last modified 2018-09-13

n/a:
Download fulltextPDF
External link:
Download fulltextURL
Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)