| Title:
|
Nash {\Large $\epsilon $}-equilibria for stochastic games with total reward functions: an approach through Markov decision processes (English) |
| Author:
|
González-Padilla, Francisco J. |
| Author:
|
Montes-de-Oca, Raúl |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
152-165 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
stochastic games |
| Keyword:
|
Nash equilibrium |
| Keyword:
|
Markov decision processes |
| Keyword:
|
total rewards |
| MSC:
|
90C40 |
| MSC:
|
91A15 |
| MSC:
|
91A50 |
| idZBL:
|
Zbl 07088883 |
| idMR:
|
MR3935419 |
| DOI:
|
10.14736/kyb-2019-1-0152 |
| . |
| Date available:
|
2019-05-07T11:15:02Z |
| Last updated:
|
2020-02-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147710 |
| . |
| Reference:
|
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| . |
