Marginal Values of a Stochastic Game

References

• [1] Amir R (2003) Stochastic games in economics and related fields: An overview. Neyman A, Sorin S, eds. Stochastic Games and Applications (Springer, Dordrecht, Netherlands), 455–470.Crossref, Google Scholar
• [2] Attia L, Oliu-Barton M (2019) A formula for the value of a stochastic game. Proc. Natl. Acad. Sci. USA 116(52):26435–26443.Crossref, Google Scholar
• [3] Attia L, Oliu-Barton M (2021) Shapley-Snow kernels, multiparameter eigenvalue problems and stochastic games. Math. Oper. Res. 46(3):1181–1202.Link, Google Scholar
• [4] Attia L, Oliu-Barton M (2023) Stationary equilibria in discounted stochastic games. Dynam. Games Appl., ePub ahead of print March 5, https://doi.org/10.1007/s13235-023-00495-x.Crossref, Google Scholar
• [5] Beling PA (2001) Exact algorithms for linear programming over algebraic extensions. Algorithmica 31(4):459–478.Crossref, Google Scholar
• [6] Bewley T, Kohlberg E (1976) The asymptotic theory of stochastic games. Math. Oper. Res. 1:197–208.Link, Google Scholar
• [7] Bewley T, Kohlberg E (1978) On stochastic games with stationary optimal strategies. Math. Oper. Res. 3:104–125.Link, Google Scholar
• [8] Catoni O, Oliu-Barton M, Ziliotto B (2021) Constant payoff in zero-sum stochastic games. Ann. Inst. Henri Poincare Probab. Statist 57(4):1888–1900.Google Scholar
• [9] Filar J, Vrieze K (1997) Competitive Markov Decision Processes (Springer New York, New York).Google Scholar
• [10] Freidlin MI, Wentzell AD (1984) Random Perturbations of Dynamical Systems (Springer Berlin, Heidelberg, Germany).Crossref, Google Scholar
• [11] Gillette D (1957) Stochastic games with zero stop probabilities. Dresher M, Tucker AW, Wolfe P, eds. Contributions to the Theory of Games, vol. 3 (Princeton University Press, Princeton, NJ), 179–187.Google Scholar
• [12] Hardy GH, Littlewood JE (1914) Tauberian theorems concerning power series and Dirichlet’s series whose coefficients are positive. Proc. London Math. Soc. 13:174–191.Crossref, Google Scholar
• [13] Kohlberg E (1974) Repeated games with absorbing states. Ann. Statist. 2:724–738.Crossref, Google Scholar
• [14] Krantz SG, Parks HR (2013) The Implicit Function Theorem: History, Theory, and Applications (Birkhäuser, New York).Crossref, Google Scholar
• [15] Mertens J-F, Neyman A (1981) Stochastic games. Internat. J. Game Theory 10:53–66.Crossref, Google Scholar
• [16] Mills HD (1956) Marginal values of matrix games and linear programs. Kuhn HW, Tucker AW, eds. Linear Inequalities and Related Systems, Annals of Mathematics Studies, vol. 38 (Princeton University Press, Princeton, NJ), 183–193.Google Scholar
• [17] Neyman A, Sorin S (2010) Repeated games with public uncertain duration process. Internat. J. Game Theory 39:29–52.Crossref, Google Scholar
• [18] Oliu-Barton M (2014) The asymptotic value in stochastic games. Math. Oper. Res. 39:712–721.Link, Google Scholar
• [19] Oliu-Barton M (2018) The splitting game: Value and optimal strategies. Dynam. Games Appl. 8:157–179.Crossref, Google Scholar
• [20] Oliu-Barton M (2021) New algorithms for solving zero-sum stochastic games. Math. Oper. Res. 46(1):255–267.Link, Google Scholar
• [21] Oliu-Barton M (2022) Weighted-average stochastic games with constant payoff. Oper. Res. 22(3):1675–1696.Crossref, Google Scholar
• [22] Oliu-Barton M, Vigeral G (2023) Absorbing games with irrational values. Oper. Res. Lett. 51:555–559.Crossref, Google Scholar
• [23] Ostrowski A (1937) Sur la détermination des bornes inférieures pour une classe des determinants. Bull. Sci. Math. 61:19–32.Google Scholar
• [24] Puiseux V (1850) Recherches sur les fonctions algébriques. J. Math. Pures Appl. (15):365–480.Google Scholar
• [25] Rosenberg D, Sorin S (2001) An operator approach to zero-sum repeated games. Israel J. Math. 121(1):221–246.Crossref, Google Scholar
• [26] Shapley LS (1953) Stochastic games. Proc. Natl. Acad. Sci. USA 39(10):1095–1100.Crossref, Google Scholar
• [27] Shapley LS, Snow RN (1950) Basic solutions of discrete games. Kuhn HW, Tucker AW, eds. Contributions to the Theory of Games, vol. I, Annals of Mathematics Studies, vol. 24 (Princeton University Press, Princeton, NJ), 27–35.Google Scholar
• [28] Sion M (1958) On general minimax theorems. Pacific J. Math. 8:171–176.Crossref, Google Scholar
• [29] Solan E (2003) Continuity of the value of competitive Markov decision processes. J. Theoret. Probab. 16(4):831–845.Crossref, Google Scholar
• [30] Solan E, Vieille N (2015) Stochastic games. Proc. Natl. Acad. Sci. USA 112(45):13743–13746.Crossref, Google Scholar
• [31] Vigeral G (2013) A zero-sum stochastic game with compact action sets and no asymptotic value. Dynam. Games Appl. 3:172–186.Crossref, Google Scholar
• [32] Ziliotto B (2016) A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games. Math. Oper. Res. 41:1522–1534.Link, Google Scholar