Existence of stationary equilibrium strategies in non-zero sum discounted stochastic games with uncountable state space and state-independent transitions

1989 ◽  
Vol 18 (2) ◽  
pp. 189-194 ◽  
Author(s):  
T. Parthasarathy ◽  
S. Sinha
Keyword(s):  
State Space ◽  
Stochastic Games ◽  
Stationary Equilibrium ◽  
Equilibrium Strategies ◽  
Zero Sum ◽  
Uncountable State Space

scholarly journals Limit Equilibrium Payoffs in Stochastic Games

2020 ◽  
Vol 45 (3) ◽  
pp. 889-895 ◽  
Author(s):  
Jérôme Renault ◽  
Bruno Ziliotto
Keyword(s):  
Normal Form ◽  
Stochastic Games ◽  
Limit Equilibrium ◽  
Discount Factor ◽  
Stationary Equilibrium ◽  
Zero Sum

We study the limit of equilibrium payoffs, as the discount factor goes to one, in non-zero-sum stochastic games. We first show that the set of stationary equilibrium payoffs always converges. We then provide two-player examples in which the whole set of equilibrium payoffs diverges. The construction is robust to perturbations of the payoffs and to the introduction of normal-form correlation.

scholarly journals Characterization and simplification of optimal strategies in positive stochastic games

2018 ◽  
Vol 55 (3) ◽  
pp. 728-741 ◽  
Author(s):  
János Flesch ◽  
Arkadi Predtetchinski ◽  
William Sudderth
Keyword(s):  
State Space ◽  
Optimal Strategy ◽  
Stochastic Games ◽  
Optimal Strategies ◽  
Action Space ◽  
Positive Zero ◽  
Countable State ◽  
Zero Sum ◽  
Action Spaces

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.

EQUILIBRIUM STRATEGIES IN STOCHASTIC GAMES WITH ADDITIVE COST AND TRANSITION STRUCTURE

1999 ◽  
Vol 01 (02) ◽  
pp. 131-147 ◽  
Author(s):  
HEINZ-UWE KÜENLE
Keyword(s):  
Weight Function ◽  
Stochastic Games ◽  
Optimal Strategies ◽  
Cost Structure ◽  
Equilibrium Strategy ◽  
Transition Structure ◽  
Equilibrium Strategies ◽  
Zero Sum ◽  
Action Spaces ◽  
Treated State

Two-person stochastic games with additive transition and cost structure and the criterion of expected total costs are treated. State space and action spaces are standard Borel, and unbounded costs are allowed. For the zero-sum case, it is shown that there are stationary deterministic εη-optimal strategies for every ε>0 and a certain weight function η if some semi-continuity and compactness conditions are fulfilled. Using these results, the existence of so-called quasi-stationary deterministic εη-equilibrium strategy pairs under corresponding conditions is proven.

scholarly journals Zero-Sum Stochastic Games over the Field of Real Algebraic Numbers

2019 ◽  
Vol 9 (4) ◽  
pp. 1026-1041
Author(s):  
K. Avrachenkov ◽  
V. Ejov ◽  
J. A. Filar ◽  
A. Moghaddam
Keyword(s):  
Stochastic Games ◽  
Algebraic Numbers ◽  
Zero Sum
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