scholarly journals Stochastic games with metric state space

1980 ◽  
Vol 9 (1) ◽  
pp. 25-36 ◽  
Author(s):  
H. A. M. Couwenbergh
Keyword(s):  
1978 ◽  
Vol 10 (2) ◽  
pp. 452-471 ◽  
Author(s):  
A. Federgruen

This paper considers non-cooperative N-person stochastic games with a countable state space and compact metric action spaces. We concentrate upon the average return per unit time criterion for which the existence of an equilibrium policy is established under a number of recurrency conditions with respect to the transition probability matrices associated with the stationary policies. These results are obtained by establishing the existence of total discounted return equilibrium policies, for each discount factor α ∈ [0, 1) and by showing that under each one of the aforementioned recurrency conditions, average return equilibrium policies appear as limit policies of sequences of discounted return equilibrium policies, with discount factor tending to one.Finally, we review and extend the results that are known for the case where both the state space and the action spaces are finite.


1978 ◽  
Vol 10 (02) ◽  
pp. 452-471 ◽  
Author(s):  
A. Federgruen

This paper considers non-cooperative N-person stochastic games with a countable state space and compact metric action spaces. We concentrate upon the average return per unit time criterion for which the existence of an equilibrium policy is established under a number of recurrency conditions with respect to the transition probability matrices associated with the stationary policies. These results are obtained by establishing the existence of total discounted return equilibrium policies, for each discount factor α ∈ [0, 1) and by showing that under each one of the aforementioned recurrency conditions, average return equilibrium policies appear as limit policies of sequences of discounted return equilibrium policies, with discount factor tending to one. Finally, we review and extend the results that are known for the case where both the state space and the action spaces are finite.


2009 ◽  
Vol 38 (2) ◽  
pp. 263-289 ◽  
Author(s):  
János Flesch ◽  
Gijs Schoenmakers ◽  
Koos Vrieze

2018 ◽  
Vol 55 (3) ◽  
pp. 728-741 ◽  
Author(s):  
János Flesch ◽  
Arkadi Predtetchinski ◽  
William Sudderth

Abstract We consider positive zero-sum stochastic games with countable state and action spaces. For each player, we provide a characterization of those strategies that are optimal in every subgame. These characterizations are used to prove two simplification results. We show that if player 2 has an optimal strategy then he/she also has a stationary optimal strategy, and prove the same for player 1 under the assumption that the state space and player 2's action space are finite.


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