Nash $ϵ$-equilibria for stochastic games with total reward functions: an approach through Markov decision processes

González-Padilla, Francisco J., and Montes-de-Oca, Raúl. "Nash $\epsilon $-equilibria for stochastic games with total reward functions: an approach through Markov decision processes." Kybernetika 55.1 (2019): 152-165. <http://eudml.org/doc/294587>.

@article{González2019,
abstract = {The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an $\epsilon $-equilibrium. To reach this goal, the results of Markov decision processes are used to find $\epsilon $-optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani’s Fixed Point Theorem to obtain the $\epsilon $-equilibrium mentioned. Moreover, two examples to illustrate the theory developed are presented.},
author = {González-Padilla, Francisco J., Montes-de-Oca, Raúl},
journal = {Kybernetika},
keywords = {stochastic games; Nash equilibrium; Markov decision processes; total rewards},
language = {eng},
number = {1},
pages = {152-165},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Nash $\epsilon $-equilibria for stochastic games with total reward functions: an approach through Markov decision processes},
url = {http://eudml.org/doc/294587},
volume = {55},
year = {2019},
}

TY - JOUR
AU - González-Padilla, Francisco J.
AU - Montes-de-Oca, Raúl
TI - Nash $\epsilon $-equilibria for stochastic games with total reward functions: an approach through Markov decision processes
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 1
SP - 152
EP - 165
AB - The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an $\epsilon $-equilibrium. To reach this goal, the results of Markov decision processes are used to find $\epsilon $-optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani’s Fixed Point Theorem to obtain the $\epsilon $-equilibrium mentioned. Moreover, two examples to illustrate the theory developed are presented.
LA - eng
KW - stochastic games; Nash equilibrium; Markov decision processes; total rewards
UR - http://eudml.org/doc/294587
ER -