Browsing by Subject "Stochastic games"

Filter results by typing the first few letters
Now showing 1 - 3 of 3
  • Thumbnail Image
    ItemOpen Access
    Fictitious play in zero-sum stochastic games
    (Society for Industrial and Applied Mathematics, 2022) Sayin, Muhammed O.; Parise, Francesca; Ozdaglar, Asuman
    We present a novel variant of fictitious play dynamics combining classical fictitiousplay with Q-learning for stochastic games and analyze its convergence properties in two-player zero-sum stochastic games. Our dynamics involves players forming beliefs on the opponent strategyand their own continuation payoff (Q-function), and playing a greedy best response by using theestimated continuation payoffs. Players update their beliefs from observations of opponent actions.A key property of the learning dynamics is that update of the beliefs onQ-functions occurs at aslower timescale than update of the beliefs on strategies. We show that in both the model-based andmodel-free cases (without knowledge of player payoff functions and state transition probabilities),the beliefs on strategies converge to a stationary mixed Nash equilibrium of the zero-sum stochasticgame.
  • Thumbnail Image
    ItemOpen Access
    Inventory control under substitutable demand: A stochastic game application
    (John Wiley & Sons, 2002) Avsşr, Z. M.; Baykal-Gürsoy, M.
    Substitutable product inventory problem is analyzed using the concepts of stochastic game theory. It is assumed that there are two substitutable products that are sold by different retailers and the demand for each product is random. Game theoretic nature of this problem is the result of substitution between products. Since retailers compete for the substitutable demand, ordering decision of each retailer depends on the ordering decision of the other retailer. Under the discounted payoff criterion, this problem is formulated as a two‐person nonzero‐sum stochastic game. In the case of linear ordering cost, it is shown that there exists a Nash equilibrium characterized by a pair of stationary base stock strategies for the infinite horizon problem. This is the unique Nash equilibrium within the class of stationary base stock strategies.
  • Thumbnail Image
    ItemOpen Access
    Perseverance and suspense in tug-of-war
    (Elsevier, 2021-01-06) Karagözoğlu, Emin; Sağlam, Hüseyin Çağrı; Turan, A. R.
    We study a tug-of-war game between two players using the lottery contest success function (CSF) and a quadratic cost (of effort) function. We construct a pure strategy symmetric Markov perfect equilibrium of this game, show that it is unique, and provide closed-form solutions for equilibrium strategies and values. In stark contrast to a model of tug-of-war with an all-pay auction CSF, players exert positive efforts until the very last battle in this equilibrium. We deliver a set of empirically appealing results on effort dynamics.