Zero-Sum Discounted Reward Criterion Games for Piecewise Deterministic Markov Processes
Résumé
This papers dealswith the zero-sum gamewith a discounted reward criterion
for piecewise deterministic Markov process (PDMPs) in general Borel spaces. The
two players can act on the jump rate and transition measure of the process, with the
decisions being taken just after a jump of the process. The goal of this paper is to
derive conditions for the existence of min–max strategies for the infinite horizon total
expected discounted reward function, which is composed of running and boundary
parts. The basic idea is, by using the special features of the PDMPs, to re-write the
problem via an embedded discrete-time Markov chain associated to the PDMP and
re-formulate the problem as a discrete-stage zero sum game problem.