Continuous-time zero-sum games for Markov chains with risk-sensitive finite-horizon cost criterion

2021 ◽  
pp. 1-20
Author(s):  
Subrata Golui ◽  
Chandan Pal
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Finite Horizon ◽  
Zero Sum Games ◽  
Time Zero ◽  
Cost Criterion ◽  
Risk Sensitive ◽  
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.

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

2003 ◽  
Vol 40 (2) ◽  
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.

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