scholarly journals On Martingale Problems with Continuous-Time Mixing and Values of Zero-Sum Games without the Isaacs Condition

2014 ◽  
Vol 52 (5) ◽  
pp. 2877-2890 ◽  
Author(s):  
Mihai Sîrbu
Keyword(s):  
Continuous Time ◽  
Zero Sum Games ◽  
Martingale Problems ◽  
Zero Sum

Zero-sum games for continuous-time Markov chains with unbounded transition and average payoff rates

2003 ◽  
Vol 40 (02) ◽  
pp. 327-345 ◽  
Author(s):  
Xianping Guo ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Transition Rates ◽  
Zero Sum Games ◽  
Stationary Strategies ◽  
Continuous Time Markov Chains ◽  
Average Payoff ◽  
Optimal Stationary Strategies ◽  
Zero Sum

This paper is a first study of two-person zero-sum games for denumerable continuous-time Markov chains determined by given transition rates, with an average payoff criterion. The transition rates are allowed to be unbounded, and the payoff rates may have neither upper nor lower bounds. In the spirit of the ‘drift and monotonicity’ conditions for continuous-time Markov processes, we give conditions on the controlled system's primitive data under which the existence of the value of the game and a pair of strong optimal stationary strategies is ensured by using the Shapley equations. Also, we present a ‘martingale characterization’ of a pair of strong optimal stationary strategies. Our results are illustrated with a birth-and-death game.

scholarly journals Data-Driven Integral Reinforcement Learning for Continuous-Time Non-Zero-Sum Games

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 82901-82912 ◽  
Author(s):  
Yongliang Yang ◽  
Liming Wang ◽  
Hamidreza Modares ◽  
Dawei Ding ◽  
Yixin Yin ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Continuous Time ◽  
Data Driven ◽  
Zero Sum Games ◽  
Zero Sum

scholarly journals Zero-sum games for continuous-time jump Markov processes in Polish spaces: discounted payoffs

2007 ◽  
Vol 39 (03) ◽  
pp. 645-668 ◽  
Author(s):  
Xianping Guo ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Infinitesimal Operator ◽  
Polish Spaces ◽  
Zero Sum Games ◽  
Stationary Strategies ◽  
Value Of The Game ◽  
Optimal Stationary Strategies ◽  
Zero Sum ◽  
Jump Markov Processes

This paper is devoted to the study of two-person zero-sum games for continuous-time jump Markov processes with a discounted payoff criterion. The state and action spaces are all Polish spaces, the transition rates are allowed to beunbounded, and the payoff rates may haveneither upper nor lower bounds. We give conditions on the game'sprimitive dataunder which the existence of a solution to the Shapley equation is ensured. Then, from the Shapley equation, we obtain the existence of the value of the game and of a pair of optimal stationary strategies using theextended infinitesimal operatorassociated with the transition function of a possibly nonhomogeneous continuous-time jump Markov process. We also provide arecursiveway of computing (or at least approximating) the value of the game. Moreover, we present a ‘martingale characterization’ of a pair of optimal stationary strategies. Finally, we apply our results to a controlled birth and death system and a Schlögl first model, and then we use controlled Potlach processes to illustrate our conditions.

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