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Published online by Cambridge University Press:  05 May 2022

Eilon Solan
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Tel-Aviv University
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References

Altman, E., Avrachenkov, K., Bonneau, N., Debbah, M., El-Azouzi, R., and Sadoc Menasche, D. (2008) Constrained Cost-Coupled Stochastic Games with Independent State Processes, Operations Research Letters, 36, 160164.Google Scholar
Amir, R. (1996) Continuous Stochastic Games of Capital Accumulation with Convex Transitions, Games and Economic Behavior, 15(2), 111131.CrossRefGoogle Scholar
Andersson, D. and Miltersen, P. B. (2009) The Complexity of Solving Stochastic Games on Graphs. In Dong, Y., Du, D. Z., and Ibarra, O. (eds.), Algorithms and Computation, ISAAC 2009. Lecture Notes in Computer Science, vol. 5878, Springer, pp. 112121.CrossRefGoogle Scholar
Ashkenazi-Golan, G., Krasikov, I., Rainer, C., and Solan, E. (2020) Absorption Paths and Equilibria in Quitting Games. https://arxiv.org/pdf/2012.04369.pdf.Google Scholar
Attia, L. and Oliu-Barton, M. (2020) A Formula for the Value of a Stochastic Game, Proceedings of the National Academy of Sciences of the United States of America, 116(52), 2643526443.Google Scholar
Başar, T. and Olsder, G. J. (1998) Dynamic Noncooperative Game Theory, 2nd ed., Academic Press.Google Scholar
Başar, T. and Zaccour, G. (2017) Handbook of Dynamic Game Theory, Springer.Google Scholar
Benedetti, R. and Risler, J. J. (1990) Real Algebraic and Semi-Algebraic Sets, Hermann.Google Scholar
Bewley, T. and Kohlberg, E. (1976) The Asymptotic Theory of Stochastic Games, Mathematics of Operations Research, 1, 197208.Google Scholar
Bewley, T. and Kohlberg, E. (1978) On Stochastic Games with Stationary Optimal Strategies, Mathematics of Operations Research, 3, 104125.Google Scholar
Billingsley, P. (1995) Probability and Measure, John Wiley & Sons.Google Scholar
Blackwell, D. (1962) Discrete Dynamic Programming, The Annals of Mathematical Statistics, 33(2), 719726.CrossRefGoogle Scholar
Blackwell, D. (1965) Discounted Dynamic Programming, The Annals of Mathematical Statistics, 36(1), 226235.Google Scholar
Blackwell, D. and Ferguson, T. S. (1968) The Big Match, The Annals of Mathematical Statistics, 39, 159163.Google Scholar
Bochnak, J., Coste, M., and Roy, M. F. (2013) Real Algebraic Geometry, Springer Science & Business Media.Google Scholar
Bolte, J., Gaubert, S., and Vigeral, G. (2015) Definable Zero-Sum Stochastic Games, Mathematics of Operations Research, 40(1), 171191.CrossRefGoogle Scholar
Border, K. C. (1985) Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press.CrossRefGoogle Scholar
Bourque, M. and Raghavan, T. E. S. (2014) Policy Improvement for Perfect Information Additive Reward and Additive Transition Stochastic Games with Discounted and Average Payoffs, Journal of Dynamics and Games, 1(3), 347361.Google Scholar
Breton, M. (1991) Algorithms for Stochastic Games. In Raghavan, T. E. S., Ferguson, T. S., and Parthasarathy, T. (eds.), Stochastic Games and Related Topics: In Honor of Professor LS Shapley, Theory and Decision Library, Series C, Game Theory, Mathematical Programming and Operations Research, vol.7, Kluwer, pp. 4557.Google Scholar
Catoni, O., Oliu-Barton, M., and Ziliotto, B. (2021, November) Constant Payoff in Zero-Sum Stochastic Games, Annales de l’Institut Henri Poincaré (Probabilités et Statistiques), 57(4), 18881900.Google Scholar
Chakrabarti, S. K. (2003) Pure Strategy Markov Equilibrium in Stochastic Games with a Continuum of Players, Journal of Mathematical Economics, 39(7), 693724.Google Scholar
Chatterjee, K., Alfaro, L. D., and Henzinger, T. A. (2008) Termination Criteria for Solving Concurrent Safety and Reachability Games. In Matheiu, C. (ed.), Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computer Machinery and Society for Industrial and Applied Mathematics, pp. 197206.Google Scholar
Chatterjee, K., Doyen, L., and Henzinger, T. A. (2009) A Survey of Stochastic Games with Limsup and Liminf Objectives. In Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., and Thomas, W. (eds.), International Colloquium on Automata, Languages, and Programming, Springer, pp. 115.Google Scholar
Chatterjee, K., Doyen, L., and Henzinger, T. A. (2013) A Survey of Partial-Observation Stochastic Parity Games, Formal Methods in System Design, 43(2), 268284.Google Scholar
Chatterjee, K. and Henzinger, T. A. (2012) A Survey of Stochastic ω-Regular Games, Journal of Computer and System Sciences, 78, 394413.CrossRefGoogle Scholar
Chatterjee, K., Majumdar, R., and Henzinger, T. A. (2008) Stochastic Limit-Average Games Are in EXPTIME, International Journal of Game Theory, 37, 219234.CrossRefGoogle Scholar
Condon, A. (1992) The Complexity of Stochastic Games, Information and Computation, 96(2), 203224.Google Scholar
Cottle, R. W. and Dantzig, G. B. (1968) Complementary Pivot Theory of Mathematical Programming, Linear Algebra and Its Applications, 1, 103125.Google Scholar
Cottle, R. W., Pang, J. S., and Stone, R. E. (1992) The Linear Complementarity Problem,SIAM.Google Scholar
Coulomb, J. M. (2003) Stochastic Games without Perfect Monitoring, International Journal of Game Theory, 32, 7396.Google Scholar
Couwenbergh, H. A. M. (1980) Stochastic Games with Metric State Spaces, International Journal of Game Theory, 9, 2536.Google Scholar
Duffie, D., Geanakoplos, J., Mas-Colell, A., and McLennan, A. (1994) Stationary Markov Equilibria, Econometrica, 62(4), 745781.Google Scholar
Eibelshäuser, S. and Poensgen, D. (2019) Markov Quantal Response Equilibrium and a Homotopy Method for Computing and Selecting Markov Perfect Equilibria of Dynamic Stochastic Games, Preprint.Google Scholar
Eilenberg, S. and Montgomery, D. (1946) Fixed Point Theorems for Multi-Valued Transformations, American Journal of Mathematics, 68(2), 214222.CrossRefGoogle Scholar
Etessami, K., Wojtczak, D., and Yannakakis, M. (2019) Recursive Stochastic Games with Positive Rewards, Theoretical Computer Science, 777, 308328.Google Scholar
Fan, K. (1952) Fixed-Point and Minimax Theorems in Locally Convex Topological Linear Spaces, Proceedings of the National Academy of Sciences of the United States of America, 38(2), 121126.Google Scholar
Filar, J. A. and Raghavan, T. E. (1984) A Matrix Game Solution of the Single-Controller Stochastic Game, Mathematics of Operations Research, 9(3), 356362.Google Scholar
Filar, J. A. and Tolwinski, B. (1991) On the Algorithm of Pollatschek and Avi-Itzhak. In Raghavan, T. E. S., Ferguson, T. S., Parthasarathy, T., and Vrieze, O. J. (eds.), Stochastic Games and Related Topics, Kluwer, pp. 5970.Google Scholar
Filar, J. and Vrieze, K. (1997) Competitive Markov Decision Processes, Springer Science and Business Media.Google Scholar
Fink, A. M. (1964) Equilibrium in a Stochastic n-Person Game, Journal of Science of the Hiroshima University, 28, 8993.Google Scholar
Flesch, J., Schoenmakers, G., and Vrieze, K. (2008) Stochastic Games on a Product State Space, Mathematics of Operations Research, 33, 403420.Google Scholar
Flesch, J., Schoenmakers, G., and Vrieze, K. (2009) Stochastic Games on a Product State Space: The Periodic Case, International Journal of Game Theory, 38, 263289.Google Scholar
Flesch, J., Thuijsman, F., and Vrieze, K. (1996) Recursive Repeated Games with Absorbing States, Mathematics of Operations Research, 21, 10161022.Google Scholar
Flesch, J., Thuijsman, F., and Vrieze, K. (1997) Cyclic Markov Equilibria in Stochastic Games, International Journal of Game Theory, 26, 303314.Google Scholar
Fortnow, L. and Kimmel, P. (1998) Beating a Finite Automaton in the Big Match. In Moss, L.S.(ed.),Proceedings of the Seventh Conference on Theoretical Aspects of Rationality and Knowledge, Morgan Kaufmann, pp. 225234.Google Scholar
Friedlin, M. and Wentzell, A. (1984) Random Perturbations of Dynamical Systems, Springer.Google Scholar
Gensbittel, F. and Renault, J. (2015) The Value of Markov Chain Games with Incomplete Information on Both Sides, Mathematics of Operations Research, 40(4), 820841.Google Scholar
Gillette, D. (1957) Stochastic Games with Zero Stop Probabilities. In Kuhn, H. W. and Tucker, A. W. (eds.), Contributions to the Theory of Games, vol.3, Princeton University Press, pp. 179187.Google Scholar
Gimbert, H., Renault, J., Sorin, S., Venel, X., and Zielonka, W. (2016) On Values of Repeated Games with Signals, The Annals of Applied Probability, 26(1), 402424.Google Scholar
Glicksberg, I. L. (1952) A Further Generalization of the Kakutani Fixed Point Theorem, with Application to Nash Equilibrium Points, Proceedings of the American Mathematical Society, 3(1), 170174.Google Scholar
Govindan, S. and Wilson, R. (2010) A Global Newton Method to Compute Nash Equilibria, Journal of Economic Theory, 110(1), 6586.Google Scholar
Guo, X. and Hernández-Lerma, O. (2005a) Nonzero-Sum Games for Continuous-Time Markov Chains with Unbounded Discounted Payoffs, Journal of Applied Probability, 42, 303320.Google Scholar
Guo, X. and Hernández-Lerma, O. (2005b) Zero-Sum Continuous-Time Markov Games with Unbounded Transition and Discounted Payoff Rates, Bernoulli, 11(6), 10091029.CrossRefGoogle Scholar
Hansen, K. A., Ibsen-Jensen, R., and Miltersen, P. B. (2011) The Complexity of Solving Reachability Games Using Value and Strategy Iteration. In Kulikov, A. and Vereshchagin, N. (eds.), International Computer Science Symposium in Russia, Springer, pp. 7790.Google Scholar
Hansen, K. A., Ibsen-Jensen, R., and Neyman, A. (2018) The Big Match with a Clock and a Bit of Memory. In Tardos, E., Elkind, E., and Vohra, R. (eds.), Proceedings of the 2018 ACM Conference on Economics and Computation, Association for Computer Machinery, pp. 149150.CrossRefGoogle Scholar
Hansen, K. A., Ibsen-Jensen, R., and Neyman, A. (2021) Absorbing Games with a Clock and Two Bits of Memory, Games and Economic Behavior, 128, 213230.Google Scholar
Hansen, K. A., Koucky, M., Lauritzen, N., Miltersen, P. B. and Tsigaridas, E. P. (2011) Exact Algorithms for Solving Stochastic Games. In Fortnow, L. and Vadhan, S. (eds.), Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, Association for Computer Machinery, pp. 205214.Google Scholar
Harris, C., Reny, P., and Robson, A. (1995) The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization, Econometrica, 63(3), 507544.CrossRefGoogle Scholar
He, W. and Sun, Y. (2017) Stationary Markov Perfect Equilibria in Discounted Stochastic Games, Journal of Economic Theory, 169, 3561.Google Scholar
Heller, Y. (2012) Sequential Correlated Equilibria in Stopping Games, Operations Research, 60(1), 209224.Google Scholar
Herings, P. J. J. and Peeters, R. J. A. P. (2004) Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation, Journal of Economic Theory, 118, 3260.Google Scholar
Hörner, J., Rosenberg, D., Solan, E., and Vieille, N. (2010) On a Markov Game with One-Sided Information, Operations Research, 58, 11071115.Google Scholar
Horst, U. (2005) Stationary Equilibria in Discounted Stochastic Games with Weakly Interacting Players, Games and Economic Behavior, 51, 83108.CrossRefGoogle Scholar
Jaśkiewicz, A. and Nowak, A. S. (2005) Nonzero-Sum Semi-Markov Games with the Expected Average Payoffs, Mathematical Methods of Operations Research, 62, 2340.Google Scholar
Jaśkiewicz, A. and Nowak, A. S. (2006) Zero-Sum Ergodic Stochastic Games with Feller Transition Probabilities, SIAM Journal on Control and Optimization, 45, 773789.Google Scholar
Jaśkiewicz, A. and Nowak, A. S. (2011) Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics, Dynamic Games and Their Applications, 1, 253279.Google Scholar
Jaśkiewicz, A. and Nowak, A. S. (2018a) Zero-Sum Stochastic Games. In Başar, T. and Zaccour, G. (eds.), Handbook of Dynamic Game Theory, vol. 1, Springer, pp. 165.Google Scholar
Jaśkiewicz, A. and Nowak, A. S. (2018b) Non-Zero-Sum Stochastic Games. In Başar, T. and Zaccour, G. (eds.) Handbook of Dynamic Game Theory, vol. 1, Springer, pp. 281344.CrossRefGoogle Scholar
Jasso-Fuentes, H. (2005) Noncooperative Continuous-Time Markov Games, Morfismos, 9, 3954.Google Scholar
Jovanovic, B. and Rosenthal, R. W. (1988) Anonymous Sequential Games, Journal of Mathematical Economics, 17(1), 7787.Google Scholar
Jurdziński, M., Paterson, M., and Zwick, U. (2008) A Deterministic Subexponential Algorithm for Solving Parity Games, SIAM Journal on Computing, 38(4), 15191532.Google Scholar
Kakutani, S. (1941) A Generalization of Brouwer’s Fixed Point Theorem, Duke Mathematical Journal, 8(3), 457459.Google Scholar
Khan, M. A. and Sun, Y. (2002) Non-Cooperative Games with Many Players. In Aumann, R. and Hart, S. (eds.), Handbook of Game Theory with Economic Applications, vol. 3, North Holland, pp. 17611808.Google Scholar
Kocel-Cynk, B., Pawłucki, W., and Valette, A. (2014) A Short Geometric Proof that Hausdorff Limits Are Definable in any O-minimal Structure, Advances in Geometry, 14(1), 4958.CrossRefGoogle Scholar
Kohlberg, E. (1974) Repeated Games with Absorbing States, The Annals of Statistics, 2(4), 724738.Google Scholar
Korevaar, J. (2004) Tauberian Theory: A Century of Developments, Springer.Google Scholar
Kumar, P. R. and Shiau, T. H. (1981) Existence of Value and Randomized Strategies in Zero-Sum Discrete Time Stochastic Dynamic Games, SIAM Journal on Control and Optimization, 19, 617634.Google Scholar
Laraki, R. and Sorin, S. (2015) Advances in Zero-Sum Dynamic Games. In Aumann, R. J. and Hart, S. (eds.), Handbook of Game Theory with Economic Applications, vol. 4, Elsevier, pp. 2794.Google Scholar
Lehrer, E. and Monderer, D. (1994) Discounting versus Averaging in Dynamic Programming, Games and Economic Behavior, 6, 97113.Google Scholar
Lehrer, E., Solan, E., and Solan, O. N. (2016) The Value Functions of Markov Decision Processes, Operations Research Letters, 44, 587591.Google Scholar
Lehrer, E. and Sorin, S. (1992) A Uniform Tauberian Theorem in Dynamic Programming, Mathematics of Operations Research, 17, 303307.Google Scholar
Levy, Y. (2013a) Discounted Stochastic Games with No Stationary Nash Equilibrium: Two Examples, Econometrica, 81(5), 19732007.Google Scholar
Levy, Y. (2013b) Continuous-Time Stochastic Games of Fixed Duration, Dynamic Games and Applications, 3(2), 279312.CrossRefGoogle Scholar
Levy, Y. J. and McLennan, A. (2015) Corrigendum to “Discounted Stochastic Games with No Stationary Nash Equilibrium: Two Examples,Econometrica, 83(3), 12371252.Google Scholar
Liggett, T. M. and Lippman, S. A. (1969) Stochastic Games with Perfect Information and Time Average Payoff, SIAM Review, 11, 604607.Google Scholar
Maitra, A. and Parthasarathy, T. (1970) On Stochastic Games, Journal of Optimization Theory and Applications, 5, 289300.Google Scholar
Maitra, A. and Sudderth, W. (1993) Borel Stochastic Games with Lim sup Payoff, The Annals of Probability, 21, 861885.Google Scholar
Maitra, A. and Sudderth, W. (1998) Finitely Additive Stochastic Games with Borel Measurable Payoffs, International Journal of Game Theory, 27(2), 257267.Google Scholar
Maitra, A. and Sudderth, W. (2012) Discrete Gambling and Stochastic Games, Springer Science and Business Media.Google Scholar
Maschler, M. (1967) The Inspector’s Non-Constant-Sum Game: Its Dependence on a System of Detectors, Naval Research Logistics Quarterly, 14(3), 275290.Google Scholar
Maschler, M., Solan, E., and Zamir, S. (2020) Game Theory, Cambridge University Press.Google Scholar
Mashiah-Yaakovi, A. (2014) Subgame Perfect Equilibria in Stopping Games, International Journal of Game Theory, 43(1), 89135.CrossRefGoogle Scholar
Mertens, J. F. (2002) Stochastic Games. In Aumann, R. J. and Hart, S. (eds.), Handbook of Game Theory with Economic Applications, vol. 3, Elsevier, pp. 18091832.Google Scholar
Mertens, J. F. and Neyman, A. (1981) Stochastic Games, International Journal of Game Theory, 10, 5366.Google Scholar
Mertens, J. F. and Parthasarathy, T. (1987) Equilibria for Discounted Stochastic Games, CORE Discussion Paper No. 8750. Also published in Neyman, A. and Sorin, S. (eds.), Stochastic Games and Applications, NATO Science Series, Kluwer, pp. 131–172.Google Scholar
Mertens, J. F., Sorin, S., and Zamir, S. (2015) Repeated Games, Cambridge University Press.Google Scholar
Monderer, D. and Sorin, S. (1993) Asymptotic Properties in Dynamic Programming, International Journal of Game Theory, 22, 111.Google Scholar
Nash, J. F. (1950) Equilibrium points in n-person games, Proceedings of the National Academy of Sciences of the United States of America, 36(1), 4849.Google Scholar
Neumann, J. V. (1928) Zur theorie der gesellschaftsspiele. Mathematische Annalen, 100(1), 295320.Google Scholar
Neyman, A. (2013) Stochastic Games with Short-Stage Duration, Dynamic Games and Applications, 3, 236278.Google Scholar
Neyman, A. (2017) Continuous-Time Stochastic Games, Games and Economic Behavior, 104, 92130.Google Scholar
Neyman, A. and Sorin, S. (eds.) (2003) Stochastic Games and Applications, Springer Science and Business Media.Google Scholar
Nowak, A. S. (1985a) Existence of Equilibrium Stationary Strategies in Discounted Noncooperative Stochastic Games with Uncountable State Space, Journal of Optimization Theory and Applications, 45, 591620.Google Scholar
Nowak, A. S. (1985b) Universally Measurable Strategies in Zero-Sum Stochastic Games, Annals of Probability, 13(1), 269287.Google Scholar
Nowak, A. S. (1986) Semicontinuous Nonstationary Stochastic Games, Journal of Mathematical Analysis and Applications, 117, 8499.Google Scholar
Nowak, A. S. (2003a) Zero-Sum Stochastic Games with Borel State Space. In Neyman, A. and Sorin, S. (eds.), Stochastic Games and Applications, NATO Science Series, Kluwer, pp. 7791.Google Scholar
Nowak, A. S. (2003b) N-Person Stochastic Games: Extensions of the Finite State Space Case and Correlation. In Neyman, A. and Sorin, S. (eds.), Stochastic Games and Applications, NATO Science Series, Kluwer, pp. 93106.Google Scholar
Nowak, A. S. (2003c) On a New Class of Nonzero-Sum Discounted Stochastic Games Having Stationary Nash Equilibrium Points, International Journal of Game Theory, 32, 121132.Google Scholar
Nowak, A. S., and Raghavan, T. E. S. (1992) Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games, Mathematics of Operations Research, 17(3), 519526.Google Scholar
Nowak, A. S. and Raghavan, T. E. S. (1993) A Finite Step Algorithm via a Bimatrix Game to a Single Controller Non-Zero Sum Stochastic Game, Mathematical Programming, 59(1–3), 249259.Google Scholar
Oliu-Barton, M. (2014) The Asymptotic Value in Finite Stochastic Games, Mathematics of Operations Research, 39(3), 712721.Google Scholar
Oliu-Barton, M. (2020) New Algorithms for Solving Zero-Sum Stochastic Games, Mathematics of Operations Research, 46(1), 255267.Google Scholar
Parthasarathy, T. and Raghavan, T. E. S. (1981) An Orderfield Property for Stochastic Games when One Player Controls Transition Probabilities, Journal of Optimization Theory and Applications, 33, 375392.CrossRefGoogle Scholar
Parthasarathy, T. and Sinha, S. (1989) Existence of Stationary Equilibrium Strategies in Non-Zero Sum Discounted Stochastic Games with Uncountable State Space and State-Independent Transitions, International Journal of Game Theory, 18(2), 189194.Google Scholar
Peleg, B. (1969) Equilibrium Points for Games with Infinitely Many Players, Journal of the London Mathematical Society, 1–44, 292294.Google Scholar
Puterman, M. L. (1994) Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley.Google Scholar
Raghavan, T. E. S. (2003) Finite-Step Algorithms for Single-Controller and Perfect Information Stochastic Games. In Neyman, A. and Sorin, S. (eds.), Stochastic Games and Applications, Kluwer, pp. 227251.Google Scholar
Raghavan, T. E. S., Ferguson, T. S., and Parthasarathy, T. (1991) Stochastic Games and Related Topics: In Honor of Professor LS Shapley, Theory and Decision Library, Series, C, Game Theory. Mathematical Programming and Operations Research, vol. 7, Kluwer.Google Scholar
Raghavan, T. E. S. and Filar, J. A. (1991) Algorithms for Stochastic Games – A Survey, ZOR – Methods and Models of Operations Research, 35, 437472.Google Scholar
Raghavan, T. E. S. and Syed, Z. (2002) Computing Stationary Nash Equilibria of Undiscounted Single-Controller Stochastic Games, Mathematics of Operations Research, 27(2), 384400.Google Scholar
Raghavan, T. E. S. and Syed, Z. (2003) A Policy-Improvement Type Algorithm for Solving Zero-Sum Two-Person Stochastic Games of Perfect Information, Mathematical Programming, Series. A, 95, 513532.Google Scholar
Ramsey, F. P. (1930) On a Problem of Formal Logic, Proceedings of the London Mathematical Society, 30, 264286.Google Scholar
Renault, J. (2006) The Value of Markov Chain Games with Lack of Information on One Side, Mathematics of Operations Research, 31, 490512.Google Scholar
Renault, J. (2011) Uniform Value in Dynamic Programming, Journal of the European Mathematical Society, 13, 309330.Google Scholar
Renault, J. (2012) The Value of Repeated Games with an Informed Controller, Mathematics of Operations Research, 37(1), 154179.Google Scholar
Renault, J. (2014) General Limit Value in Dynamic Programming, Journal of Dynamics and Games, 1(3), 471484.Google Scholar
Renault, J. (2019) A Tutorial on Zero-Sum Stochastic Games, arXiv:1905.06577.Google Scholar
Renault, J. and Venel, X. (2017) Long-Term Values in Markov Decision Processes and Repeated Games, and a New Distance for Probability Spaces, Mathematics of Operations Research, 42(2), 349376.Google Scholar
Renault, J. and Ziliotto, B. (2020a) Limit Equilibrium Payoffs in Stochastic Games, Mathematics of Operations Research, 45(3), 889895.Google Scholar
Renault, J. and Ziliotto, B. (2020b) Hidden Stochastic Games and Limit Equilibrium Payoffs, Games and Economic Behavior, 124, 122139.Google Scholar
Rosenberg, D., Solan, E., and Vieille, N. (2002) Blackwell Optimality in Markov Decision Processes with Partial Observation, The Annals of Statistics, 30, 11781193.Google Scholar
Rosenberg, D., Solan, E., and Vieille, N. (2003) The MaxMin of Stochastic Games with Imperfect Monitoring, International Journal of Game Theory, 32, 133150.Google Scholar
Rosenberg, D., Solan, E., and Vieille, N. (2004) Stochastic Games with a Single Controller and Incomplete Information, SIAM Journal on Control and Optimization, 43 , 86110.Google Scholar
Rosenberg, D., Solan, E., and Vieille, N. (2009) Protocol with No Acknowledgement, Operations Research, 57, 905915.Google Scholar
Ross, S. M. (1982) Introduction to Stochastic Dynamic Programming, Academic Press.Google Scholar
Shapley, L. S. (1953) Stochastic Games, Proceedings of the National Academy of Sciences of the United States of America, 39, 10951100.Google Scholar
Shiryaev, A. N. (1995) Probability, Springer.Google Scholar
Shmaya, E. and Solan, E. (2004) Two-Player NonZero-Sum Stopping Games in Discrete Time, The Annals of Probability, 32(3B), 27332764.Google Scholar
Simon, R. S. (2006) Value and Perfection in Stochastic Games, Israel Journal of Mathematics, 156(1), 285309.Google Scholar
Simon, R. S. (2007) The Structure of Non-Zero-Sum Stochastic Games, Advances in Applied Mathematics, 38, 126.Google Scholar
Simon, R. S. (2012) A Topological Approach to Quitting Games, Mathematics of Operations Research, 37, 180195.Google Scholar
Simon, R. S. (2016) The Challenge of Non-Zero-Sum Stochastic Games, International Journal of Game Theory, 45(1–2), 191204.Google Scholar
Solan, E. (1998) Discounted Stochastic Games, Mathematics of Operations Research, 23, 10101021.Google Scholar
Solan, E. (1999) Three-Player Absorbing Games, Mathematics of Operations Research, 24(3), 669698.Google Scholar
Solan, E. (2003) Continuity of the Value in Competitive Markov Decision Processes, Journal of Theoretical Probability, 16, 831845.Google Scholar
Solan, E. (2008) Stochastic Games. In Liu, L. and Tamer Özsu, M. (eds.), Encyclopedia of Database Systems, Springer.Google Scholar
Solan, E. and Solan, O. N. (2020) Quitting Games and Linear Complementarity Problems, Mathematics of Operations Research, 45(2), 434454.Google Scholar
Solan, E. and Solan, O. N. (2021) Sunspot Equilibrium in Positive Recursive General Quitting Games. International Journal of Game Theory, 50, 119.Google Scholar
Solan, E., Solan, O. N., and Solan, R. (2020) Jointly Controlled Lotteries with Biased Coins, Games and Economic Behavior, 119(2020), 383391.Google Scholar
Solan, E. and Vieille, N. (2001) Quitting Games, Mathematics of Operations Research, 26, 265285.Google Scholar
Solan, E. and Vieille, N. (2002) Correlated Equilibrium in Stochastic Games, Games and Economic Behavior, 38, 362399.Google Scholar
Solan, E. and Vieille, N. (2010) Computing Uniform Optimal Strategies in Two-Player Stochastic Games, Economic Theory, 42, 237253.Google Scholar
Solan, E. and Vieille, N. (2015) Stochastic Games: A Perspective, Proceedings of the National Academy of Sciences of the United States of America, 112(45), 1374313746.Google Scholar
Solan, E. and Vohra, R. (2001) Correlated Equilibrium in Quitting Games, Mathematics of Operations Research, 26, 601610.Google Scholar
Solan, E. and Vohra, R. (2002) Correlated Equilibrium Payoffs and Public Signalling in Absorbing Games, International Journal of Game Theory, 31, 91121.Google Scholar
Solan, E. and Ziliotto, B. (2016) Stochastic Games with Signals. In Thuijsman, F. and Wagener, F. (eds.), Advances in Dynamic and Evolutionary Games, Birkhäuser, pp. 7794.Google Scholar
Sorin, S. (1986) Asymptotic Properties of a Non-Zerosum Stochastic Games, International Journal of Game Theory, 15, 101107.Google Scholar
Sorin, S. (2002) A First Course on Zero-Sum Repeated Games, Mathématiques and Applications, vol. 37, Springer-Verlag.Google Scholar
Sorin, S., Venel, X., and Vigeral, G. (2010) Asymptotic Properties of Optimal Trajectories in Dynamic Programming, Sankhya: The Indian Journal of Statistics A, 72(1), 237245.Google Scholar
Sorin, S. and Vigeral, G. (2015) Reversibility and Oscillations in Zero-Sum Discounted Stochastic Games, Journal of Dynamic Games, 2(1), 103115.Google Scholar
Szczechla, W. W., Connell, S. A., Filar, J. A., and Vrieze, O. J. (1997) On the Puiseux Series Expansion of the Limit Discount Equation of Stochastic Games, SIAM Journal on Control and Optimization, 35(3), 860875.Google Scholar
Takahashi, M. (1964) Stochastic Games with Infinitely Many Strategies, Journal of Science of the Hiroshima University Series A-I, 26, 123134.Google Scholar
Thuijsman, F. and Raghavan, T. E. S. (1997) Perfect Information Stochastic Games and Related Classes, International Journal of Game Theory, 26(3), 403408.Google Scholar
Thuijsman, F. and Vrieze, O. J. (1991) Easy Initial States in Stochastic Games. In Raghavan, T. E. S., Ferguson, T. S., Parthasarathy, T., and Vrieze, O. J. (eds.), Stochastic Games and Related Topics, Kluwer, pp. 85100.Google Scholar
Venel, X. and Ziliotto, B. (2016) Strong Uniform Value in Gambling Houses and Partially Observable Markov Decision Processes, SIAM Journal on Control and Optimization, 54(4), 19832008.Google Scholar
Vieille, N. (2000a) Equilibrium in 2-Person Stochastic Games I: A Reduction, Israel Journal of Mathematics, 119, 5591.Google Scholar
Vieille, N. (2000b) Equilibrium in 2-Person Stochastic Games I: The Case of Recursive Games, Israel Journal of Mathematics, 119, 93126.Google Scholar
Vieille, N. (2000c) Large Deviations and Stochastic Games, Israel Journal of Mathematics, 119, 127144.Google Scholar
Vieille, N. (2000d) Solvable States in n-Player Stochastic Games, SIAM Journal on Control and Optimization, 38(6), 17941804.Google Scholar
Vieille, N. (2002) Stochastic Games: Recent Results. In Aumann, R. J. and Hart, S. (eds.), Handbook of Game Theory with Economic Applications, vol.3,Elsevier, pp. 18331850.Google Scholar
Vigeral, G. (2013) A Zero-Sum Stochastic Game with Compact Action Sets and No Asymptotic Value, Dynamic Games and Their Applications, 3, 172186.Google Scholar
Vrieze, O. J. and Thuijsman, F. (1989) On Equilibria in Repeated Games with Absorbing States, International Journal of Game Theory, 18, 293310.Google Scholar
Vrieze, O. J., Tijs, S. H., Raghavan, T. E. S., and Filar, J. A. (1983) A Finite Algorithm for the Switching Control Stochastic Game, Operations-Research-Spektrum, 5(1), 1524.Google Scholar
Wei, Q. and Chen, X. (2016) Stochastic Games for Continuous-Time Jump Processes under Finite-Horizon Payoff Criterion, Applied Mathematics and Optimization, 74, 273301.Google Scholar
Zachrisson, L. E. (1964) Markov Games. In Auslander, L. A. and Aumann, R. J. (eds.), Advances in Game Theory, Princeton University Press, pp. 211253.Google Scholar
Zhang, W. (2018) Continuous-Time Constrained Stochastic Games under the Discounted Cost Criteria, Applied Mathematics and Optimization, 77, 275296.Google Scholar
Ziliotto, B. (2016a) A Tauberian Theorem for Nonexpansive Operators and Applications to Zero-Sum Stochastic Games, Mathematics of Operations Research, 41(4), 15221534.Google Scholar
Ziliotto, B. (2016b) General Limit Value in Zero-Sum Stochastic Games, International Journal of Game Theory, 45(1–2), 353374.Google Scholar
Ziliotto, B. (2016c) Zero-Sum Repeated Games: Counterexamples to the Existence of the Asymptotic Value and the Conjecture maxmin = lim vn, The Annals of Probability, 44(2), 11071133.Google Scholar
Ziliotto, B. (2018) Tauberian Theorems for General Iterations of Operators: Applications to Zero-Sum Stochastic Games, Games and Economic Behavior, 108, 486503.Google Scholar
Zwick, U. and Paterson, M. (1996) The Complexity of Mean Payoff Games on Graphs, Theoretical Computer Science, 158(1–2), 343359.Google Scholar

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  • References
  • Eilon Solan, Tel-Aviv University
  • Book: A Course in Stochastic Game Theory
  • Online publication: 05 May 2022
  • Chapter DOI: https://doi.org/10.1017/9781009029704.015
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  • References
  • Eilon Solan, Tel-Aviv University
  • Book: A Course in Stochastic Game Theory
  • Online publication: 05 May 2022
  • Chapter DOI: https://doi.org/10.1017/9781009029704.015
Available formats
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  • References
  • Eilon Solan, Tel-Aviv University
  • Book: A Course in Stochastic Game Theory
  • Online publication: 05 May 2022
  • Chapter DOI: https://doi.org/10.1017/9781009029704.015
Available formats
×