This paper deals with two-person stochastic games of resource extraction under both the discounted and the mean payoff criterion. Under some concavity and additivity assumptions concerning the payoff and the transition probability function a stationary Nash equilibrium is shown to exist. The proof is based on Schauder-Tychonoff's fixed point theorem, applied to a suitable payoff vector space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-24,
author = {P. Szajowski},
title = {Existence of Nash equilibria in two-person stochastic games of resource extraction},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {291-302},
zbl = {1255.91032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-24}
}
P. Szajowski. Existence of Nash equilibria in two-person stochastic games of resource extraction. Banach Center Publications, Tome 72 (2006) pp. 291-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-24/