Zero-Sum Discounted Reward Criterion Games for Piecewise Deterministic Markov Processes

Author(s)

Costa, O. L. V. ^[1] ; Dufour, F. ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Engn Telecomunicacoes & Controle, Escola Politecn, BR-05508900 Sao Paulo - Brazil

^[2] INRIA Bordeaux Sud Ouest, Inst Polytech Bordeaux, Inst Math Bordeaux, 200 Ave Vieille Tour, F-33405 Talence - France

• Document type: Journal article
• Source: APPLIED MATHEMATICS AND OPTIMIZATION; v. 78, n. 3, p. 587-611, DEC 2018.
• Web of Science Citations: 0

Abstract

This papers deals with the zero-sum game with 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. (AU)

• FAPESP's process: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Grantee: Julio Romano Meneghini
• Support Opportunities: Research Grants - Research Centers in Engineering Program
• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants