Continuous-time Zero-Sum Stochastic Game with Stopping and Control

DOI10.1016/J.ORL.2020.08.012arXiv2006.01420MaRDI QIDQ6341888

Publication date: 2 June 2020

Abstract: We consider a zero-sum stochastic game for continuous-time Markov chain with countable state space and unbounded transition and pay-off rates. The additional feature of the game is that the controllers together with taking actions are also allowed to stop the process. Under suitable hypothesis we show that the game has a value and it is the unique solution of certain dynamic programming inequalities with bilateral constraints. In the process we also prescribe a saddle point equilibrium.

Mathematics Subject Classification ID

Stopping times; optimal stopping problems; gambling theory (60G40) Stochastic games, stochastic differential games (91A15) Games of timing (91A55)

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