Abstract
In repeated games where the payoff is accumulated along the play, the players face a problem since they have to take into account the impact of their choices both on the current payoff and on the future of the game.
Prepared for a plenary lecture at the International Symposium on Dynamic Games and Applications, Adelaide, Australia, December 18–21, 2000.
Chapter PDF
References
Aumann R.J. and Maschler M. (1995), Repeated Games with Incomplete Information, M.I.T. Press (with the collaboration of R. Stearns).
Bewley T. and Kohlberg E. (1976a), The asymptotic theory of stochastic games, Mathematics of Operations Research, 1, 197–208.
Bewley T. and Kohlberg E. (1976b), The asymptotic solution of a recursion equation occurring in stochastic games, Mathematics of Operations Research, 1, 321–336.
Blackwell D. (1956), An analog of the minmax theorem for vector payoffs, Pacific Journal of Mathematics, 6, 1–8.
Blackwell D. and Ferguson T. (1968), The Big Match, Annals of Mathematical Statistics, 39, 159–163.
Coulomb J.-M. (1992), Repeated games with absorbing states and no signals, International Journal of Game Theory, 21, 161–174.
Coulomb J.-M. (1996), A note on ‘Big Match’, ESAIM: Probability and Statistics, 1, 89–93, http://www.edpsciences.com/ps/.
Coulomb, J.-M. (1999), Generalized Big Match, Mathematics of Operations Research, 24, 795–816.
Coulomb, J.-M. (2001), Repeated games with absorbing states and signaling structure, Mathematics of Operations Research, 26, 286–303.
De Meyer B. (1996a), Repeated games and partial differential equations, Mathematics of Operations Research, 21, 209–236.
De Meyer B. (1996b), Repeated games, duality and the Central Limit theorem, Mathematics of Operations Research, 21, 237–251.
De Meyer B. (1999), From repeated games to Brownian games, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 35, 1–48.
De Meyer B. and Rosenberg D. (1999), “Cav u” and the dual game, Mathematics of Operations Research, 24, 619–626.
Everett H. (1957), Recursive games, in Contributions to the Theory of Games, III, M. Dresher, A.W. Tucker and P. Wolfe (eds.), Annals of Mathematical Studies, 39, Princeton University Press, 47–78.
Kohlberg E. (1974), Repeated games with absorbing states, Annals of Statistics, 2, 724–738.
Kohlberg E. and Neyman A. (1981), Asymptotic behavior of non expansive mappings in normed linear spaces, Israel Journal of Mathematics, 38, 269–275.
Laraki R. (2000), Duality and games with incomplete information, preprint.
Laraki R. (2001a), Variational inequalities, systems of functional equations and incomplete information repeated games, SIAM Journal of Control and Optimization, 40, 516–524.
Laraki R. (2001b), The splitting game and applications, International Journal of Game Theory, 30, 359–376.
Laraki R. (2002), Repeated games with lack of information on one side: the dual differential approach, Mathematics of Operations Research, 27, 419–440.
Lehrer E. and Monderer D. (1994), Discounting versus averaging in dynamic programming, Games and Economic Behavior, 6, 97–113.
Lehrer E. and Sorin S. (1992), A uniform Tauberian theorem in dynamic programming, Mathematics of Operations Research, 17, 303–307.
Maitra A. and Sudderth W. (1998), Finitely additive stochastic games with Borel measurable payoffs, International Journal of Game Theory, 27, 257–267.
Mertens J.-F. (1972), The value of two-person zero-sum repeated games: the extensive case, International Journal of Game Theory, 1, 217–227.
Mertens J.-F. (1987), Repeated games, in Proceedings of the International Congress of Mathematicians, Berkeley, 1986, A.M. Gleason (ed.), American Mathematical Society, 1528–1577.
Mertens J.-F. (1998), The speed of convergence in repeated games with incomplete information on one side, International Journal of Game Theory, 27, 343–359.
Mertens J.-F. (2002), Stochastic games, in Handbook of Game Theory, 3, R. J. Aumann and S. Hart (eds.), North-Holland, 1809–1832.
Mertens J.-F. and Neyman A. (1981), Stochastic games, International Journal of Game Theory, 10, 53–66.
Mertens J.-F., S. Sorin and Zamir S. (1994), Repeated Games, CORE D.P. 9420-21-22.
Mertens J.-F. and Zamir S. (1971), The value of two-person zero-sum repeated games with lack of information on both sides, International Journal of Game Theory, 1, 39–64.
Mertens J.-F. and Zamir S. (1976a), The normal distribution and repeated games, International Journal of Game Theory, 5, 187–197.
Mertens J.-F. and Zamir S. (1976b), On a repeated game without a recursive structure, International Journal of Game Theory, 5, 173–182.
Mertens J.-F. and Zamir S. (1985), Formulation of Bayesian analysis for games with incomplete information, International Journal of Game Theory, 14, 1–29.
Mills H. D. (1956), Marginal values of matrix games and linear programs, in Linear Inequalities and Related Systems, H.W. Kuhn and A.W. Tucker (eds.), Annals of Mathematical Studies, 38, Princeton University Press, 183–193.
Monderer D. and Sorin S. (1993), Asymptotic properties in dynamic programming, International Journal of Game Theory, 22, 1–11.
Neyman A. (2003), Stochastic games and non-expansive maps, Chapter 26 in Stochastic Games and Applications, A. Neyman and S. Sorin (eds.), NATO Science Series C 570, Kluwer Academic Publishers.
Neyman A. and Sorin S. (2001), Zero-sum two-person games with public uncertain duration process, Cahier du Laboratoire d’Econometrie, Ecole Polytechnique, 2001-013.
Ponssard J.-P. and Sorin S. (1982), Optimal behavioral strategies in zero-sum games with almost perfect information, Mathematics of Operations Research, 7, 14–31.
Rosenberg D. (1998), Duality and Markovian strategies, International Journal of Game Theory, 27, 577–597.
Rosenberg D. (2000) Zero-sum absorbing games with incomplete information on one side: asymptotic analysis, SIAM Journal on Control and Optimization, 39, 208–225.
Rosenberg D. and Sorin S. (2001), An operator approach to zero-sum repeated games, Israel Journal of Mathematics, 121, 221–246.
Rosenberg D. and Vieille N. (2000), The maxmin of recursive games with lack of information on one side, Mathematics of Operations Research, 25, 23–35.
Shapley L. S. (1953), Stochastic games, Proceedings of the National Academy of Sciences of the U.S.A, 39, 1095–1100.
Sorin S. (1984), Big Match with lack of information on one side (Part I), International Journal of Game Theory, 13, 201–255.
Sorin S. (1985), Big Match with lack of information on one side (Part II), International Journal of Game Theory, 14, 173–204.
Sorin S. (1989), On repeated games without a recursive structure: existence of lim v n, International Journal of Game Theory, 18, 45–55.
Sorin S. (2002), A First Course on Zero-Sum Repeated Games, Springer.
Sorin S. (2003), The operator approach to zero-sum stochastic games, Chapter 27 in Stochastic Games and Applications, A. Neyman and S. Sorin (eds.), NATO Science Series C 570, Kluwer Academic Publishers.
Sorin S. (2004), Asymptotic properties of monotonic non-expansive mappings, Discrete Events Dynamic Systems, 14, 109–122.
Souganidis P.E. (1985), Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, Journal of Differential Equations, 17, 781–791.
Souganidis P.E. (1999), Two player zero sum differential games and viscosity solutions, in Stochastic and Differential Games, M. Bardi, T.E.S. Raghavan and T. Parthasarathy (eds.), Birkhauser, 70–104.
Vieille N. (1992), Weak approachability, Mathematics of Operations Research, 17, 781–791.
Waternaux C. (1983), Solution for a class of repeated games without recursive structure, International Journal of Game Theory, 12, 129–160.
Zamir S. (1973), On the notion of value for games with infinitely many stages, Annals of Statistics, 1, 791–796.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Birkhäuser Boston
About this chapter
Cite this chapter
Sorin, S. (2005). New Approaches and Recent Advances in Two-Person Zero-Sum Repeated Games. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_4
Download citation
DOI: https://doi.org/10.1007/0-8176-4429-6_4
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4362-1
Online ISBN: 978-0-8176-4429-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)