Summary
We deal with stochastic games with finite state and action spaces for which we examine players' possibilities for playing limiting average (ɛ-)optimal by means of stationary strategies (ɛ > 0). It is well-known that stationary limiting averageɛ-optimal strategies need not exist for all initial states, hence we focus on those particular initial states for which the limiting average value is either maximal or minimal over the set of states.
Zusammenfassung
Für stochastische Zwei-Personen-Null-Summen-Spiele mit endlichen Zustands-und Aktions-Räumen untersuchen wir die Möglichkeiten eines Spielers, um mit Hilfe von stationären Strategienɛ - optimal zu spielen bezüglich des DurchschnittsgewinnKriteriums (ɛ > 0). Es ist bekannt, daß solches im allgemeinen nicht für alle Zustände möglich ist. Deshalb konzentrieren wir unsere Untersuchung auf die Zustände für welche der Durchschnittsgewinn-Wert entweder maximal oder minimal ist.
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Thuijsman, F., Vrieze, K. Stationary ɛ-optimal strategies in stochastic games. OR Spektrum 15, 9–15 (1993). https://doi.org/10.1007/BF01783412
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DOI: https://doi.org/10.1007/BF01783412