On Markov Games with Average Reward Criterion and Weakly Continuous Transition Probabilities

2007 ◽  
Vol 45 (6) ◽  
pp. 2156-2168 ◽  
Author(s):  
Heinz‐Uwe Küenle
Keyword(s):  
Transition Probabilities ◽  
Average Reward ◽  
Continuous Transition ◽  
Markov Games ◽  
Weakly Continuous ◽  
Average Reward Criterion ◽  
Reward Criterion

On Finding Large Sets of Rewards in Two-Player ETP–ESP Games

2020 ◽  
Vol 22 (02) ◽  
pp. 2040002
Author(s):  
Reinoud Joosten ◽  
Llea Samuel
Keyword(s):  
Stochastic Games ◽  
Transition Probabilities ◽  
Pure Strategy ◽  
Continuous Functions ◽  
Average Reward ◽  
Endogenous Stage ◽  
Large Sets ◽  
Past Action ◽  
Average Reward Criterion ◽  
Reward Criterion

Games with endogenous transition probabilities and endogenous stage payoffs (or ETP–ESP games for short) are stochastic games in which both the transition probabilities and the payoffs at any stage are continuous functions of the relative frequencies of all past action combinations chosen. We present methods to compute large sets of jointly-convergent pure-strategy rewards in two-player ETP–ESP games with communicating states under the limiting average reward criterion. Such sets are useful in determining feasible rewards in a game, and instrumental in obtaining the set of (Nash) equilibrium rewards.

scholarly journals Sample-Path Optimal Stationary Policies in Stable Markov Decision Chains with the Average Reward Criterion

2015 ◽  
Vol 52 (2) ◽  
pp. 419-440
Author(s):  
Rolando Cavazos-Cadena ◽  
Raúl Montes-De-Oca ◽  
Karel Sladký
Keyword(s):  
Sample Path ◽  
Point Of View ◽  
Average Reward ◽  
Stationary Policy ◽  
Optimality Equation ◽  
Markov Decision ◽  
Average Reward Criterion ◽  
Compact Action Sets ◽  
Path Point ◽  
Reward Criterion

This paper concerns discrete-time Markov decision chains with denumerable state and compact action sets. Besides standard continuity requirements, the main assumption on the model is that it admits a Lyapunov function ℓ. In this context the average reward criterion is analyzed from the sample-path point of view. The main conclusion is that if the expected average reward associated to ℓ2 is finite under any policy then a stationary policy obtained from the optimality equation in the standard way is sample-path average optimal in a strong sense.

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