Nonlinear programming and stationary strategies in stochastic games

1986 ◽  
Vol 34 (2) ◽  
pp. 243-247 ◽  
Author(s):  
Jerzy A. Filar ◽  
Todd A. Schultz
Keyword(s):  
Nonlinear Programming ◽  
Stochastic Games ◽  
Stationary Strategies

Existence of p-Equilibrium and Optimal Stationary Strategies in Stochastic Games

1976 ◽  
Vol 60 (1) ◽  
pp. 245 ◽  
Author(s):  
C. J. Himmelberg ◽  
T. Parthasarathy ◽  
T. E. S. Raghavan ◽  
F. S. Van Vleck
Keyword(s):  
Stochastic Games ◽  
Stationary Strategies ◽  
Optimal Stationary Strategies

scholarly journals STATIONARY STRATEGIES IN ZERO-SUM STOCHASTIC GAMES

2001 ◽  
Vol 03 (04) ◽  
pp. 283-290
Author(s):  
J. FLESCH ◽  
F. THUIJSMAN ◽  
O. J. VRIEZE
Keyword(s):  
Finite Number ◽  
Stochastic Games ◽  
Stationary Strategies ◽  
Pure Strategies ◽  
Zero Sum

We deal with zero-sum stochastic games. We demonstrate the importance of stationary strategies by showing that stationary strategies are better (in terms of the rewards they guarantee for a player, against any strategy of his opponent) than (1) pure strategies (even history-dependent ones), (2) strategies which may use only a finite number of different mixed actions in any state, and (3) strategies with finite recall. Examples are given to clarify the issues.

scholarly journals On the existence of stationary Nash equilibria in average stochastic games with finite state and action spaces

2020 ◽  
Vol 13 ◽  
pp. 304-323
Author(s):  
Dmitrii Lozovanu ◽  
◽  
Stefan Pickl ◽  
Keyword(s):  
Nash Equilibria ◽  
Stochastic Games ◽  
Optimal Strategies ◽  
Stationary Strategies ◽  
Finite State ◽  
Optimal Stationary Strategies ◽  
Action Spaces

We consider infinite n-person stochastic games with limiting average payoffs criteria for the players. The main results of the paper are concerned with the existence of stationary Nash equilibria and determining the optimal strategies of the players in the games with finite state and action spaces. We present conditions for the existence of stationary Nash equilibria in the considered games and propose an approach for determining the optimal stationary strategies of the players if such strategies exist.

Nonlinear programming and stationary equilibria in stochastic games

1991 ◽  
Vol 50 (1-3) ◽  
pp. 227-237 ◽  
Author(s):  
J. A. Filar ◽  
T. A. Schultz ◽  
F. Thuijsman ◽  
O. J. Vrieze
Keyword(s):  
Nonlinear Programming ◽  
Stochastic Games

scholarly journals On the Existence and Determining Stationary Nash Equilibria for Switching Controller Stochastic Games

2021 ◽  
Vol 14 ◽  
pp. 290-301
Author(s):  
Dmitrii Lozovanu ◽  
◽  
Stefan Pickl ◽  
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Nash Equilibria ◽  
Stochastic Games ◽  
Stochastic Game ◽  
Static Game ◽  
Stationary Strategies ◽  
Switching Controller ◽  
Optimal Stationary Strategies ◽  
Stationary Nash Equilibrium

In this paper we consider the problem of the existence and determining stationary Nash equilibria for switching controller stochastic games with discounted and average payoffs. The set of states and the set of actions in the considered games are assumed to be finite. For a switching controller stochastic game with discounted payoffs we show that all stationary equilibria can be found by using an auxiliary continuous noncooperative static game in normal form in which the payoffs are quasi-monotonic (quasi-convex and quasi-concave) with respect to the corresponding strategies of the players. Based on this we propose an approach for determining the optimal stationary strategies of the players. In the case of average payoffs for a switching controller stochastic game we also formulate an auxiliary noncooperative static game in normal form with quasi-monotonic payoffs and show that such a game possesses a Nash equilibrium if the corresponding switching controller stochastic game has a stationary Nash equilibrium.

scholarly journals Existence of $p$-equilibrium and optimal stationary strategies in stochastic games

1976 ◽  
Vol 60 (1) ◽  
pp. 245-245
Author(s):  
C. J. Himmelberg ◽  
T. Parthasarathy ◽  
T. E. S. Raghavan ◽  
F. S. Van Vleck
Keyword(s):  
Stochastic Games ◽  
Stationary Strategies ◽  
Optimal Stationary Strategies

scholarly journals New Algorithms for Solving Zero-Sum Stochastic Games

2020 ◽  
Author(s):  
Miquel Oliu-Barton
Keyword(s):  
Game Theory ◽  
Stochastic Games ◽  
Classical Model ◽  
Solution Concepts ◽  
Environment Changes ◽  
Stationary Strategies ◽  
Zero Sum ◽  
Different Levels ◽  
New Algorithms

Zero-sum stochastic games, henceforth stochastic games, are a classical model in game theory in which two opponents interact and the environment changes in response to the players’ behavior. The central solution concepts for these games are the discounted values and the value, which represent what playing the game is worth to the players for different levels of impatience. In the present manuscript, we provide algorithms for computing exact expressions for the discounted values and for the value, which are polynomial in the number of pure stationary strategies of the players. This result considerably improves all the existing algorithms.

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