Abstract
The perfect monitoring assumption is replaced by a signalling structure that models, for each player, the information about the opponent’s previous action. The value of a stochastic game may not exist any more. For the class of absorbing games, we are able to show the existence of the max min and the min max. The value does not exist if they are different.
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References
Bewley, T. and Kohlberg, E. (1976) The asymptotic theory of stochastic gamesMathematics of Operations Research 1197–208.
Bewley, T. and Kohlberg, E. (1978) On stochastic games with stationary optimal strategiesMathematics of Operations Research2, 104–125.
Blackwell, D. and Ferguson, T.S. (1968) The big matchAnnals of Mathematical Statistics39, 159–163.
Coulomb, J.M. (1992) Repeated games with absorbing states and no signalsInternational Journal of Game Theory21, 161–174.
Coulomb, J.M. (1996) A note on big matchESAIM: Probability and Statistics1, 89–93.
Coulomb, J.M. (1997) On the value of discounted stochastic games, Working Paper 275, Institute of Mathematical Economics, University of Bielefeld.
Coulomb, J.M. (1999) Generalized big-matchMathematics of Operations Research24, 795–816.
Coulomb, J.M. (2001) Repeated games with absorbing states and signaling structureMathematics of Operations Research26, 286–303.
.Coulomb, J.M. (2002) Stochastic games without perfect monitoring, submitted toInternational Journal of Game Theory.
Gillette, D. (1957) Stochastic games with zero-stop probabilities, in M. Dresher, A.W. TuckerandP. Wolfe (eds.),Contributions to the Theory of Games Vol. III, Princeton University Press, Princeton, NJ, pp. 179–187.
Kohlberg, E. (1974) Repeated games with absorbing statesAnnals of Statistics2, 724–738.
Kohlberg, E. (1975) Optimal strategies in repeated games with incomplete informationInternational Journal of Game Theory4, 7–24.
Mertens, J-F. and Neyman, A. (1981) Stochastic gamesInternational Journal of Game Theory10, 53–56.
Mertens, J-F., Sorin, S. and Zamir, S. (1994) Repeated games, CORE Discussion Papers 9420, 9421, 9422, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
Rosenberg, D., Solan, E. and Vieille, N. (2003) The maxmin value of stochastic games with imperfect monitoring, submitted toInternational Journal of Game Theory.
Shapley, L.S. (1953) Stochastic gamesProceedings of the National Academy of Sciences of the U.S.A.39, 1095–1100 (Chapter 1 in this volume).
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Coulomb, JM. (2003). Absorbing Games with a Signalling Structure. In: Neyman, A., Sorin, S. (eds) Stochastic Games and Applications. NATO Science Series, vol 570. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0189-2_22
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DOI: https://doi.org/10.1007/978-94-010-0189-2_22
Publisher Name: Springer, Dordrecht
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