Abstract
This paper considers non-cooperative two-person zero-sum undiscounted stochastic games with finite state and action spaces. It is assumed that one player governs the transition rules. We give a linear programming algorithm and show, that an optimal solution to this program corresponds to the value of the game and to optimal stationary strategies for both players. Moreover, this linear programming formulation results in an existence proof of the value and of optimal stationary strategies for both players.
Zusammenfassung
In dieser Arbeit behandeln wir nichtkooperative nichtdiskontierte stochastische Zweipersonen-Nullsummenspiele mit endlichen Zustands- und Entscheidungsräumen. Dabei setzen wir voraus, daß ein Spieler das Übergangsverhalten steuert. Wir entwickeln ein lineares Programm und zeigen, daß eine Optimallösung dieses Programms den Spielwert und optimale stationäre Strategien für beide Spieler ergibt. Darüberhinaus liefert dieses lineare Programm einen Existenzbeweis für den Spielwert und für optimale stationäre Strategien für beide Spieler.
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Vrieze, O.J. Linear programming and undiscounted stochastic games in which one player controls transitions. OR Spektrum 3, 29–35 (1981). https://doi.org/10.1007/BF01721195
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DOI: https://doi.org/10.1007/BF01721195