Abstract
A brief account is given of the Dubins and Savage theory of gambling. It is then shown how the techniques of gambling theory can be applied to two-person, zero-sum stochastic games. Most proofs are omitted because they are available elsewhere. Instead we concentrate our efforts on ideas and examples.
Research supported by National Science Foundation Grant DMS-9123358
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References
Arrow, K.J., Blackwell, D., and Girshick, M.A. (1949). Bayes and minimax solutions of sequential decision problems. Econometrica 17 213–244.
Blackwell, D. (1965). Discounted dynamic programming. Ann. Math. Stat. 36 226–235.
Blackwell, D. (1966). Positive dynamic programming. Proc. Fifth Berkeley Symp. Prob. and Stat. 1 415–418.
Blackwell, D. (1969). Infinite G δ games with imperfect information. Zastosowania Matematyki 10 99–101.
Blackwell, D. (1989). Operator solution of G δ games of imperfect information. Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin, T.W. Anderson, K. Athreya, and D.L. Iglehart, Eds., Academic Press, New York.
Dubins, L.E. and Savage, L.J. (1965). How to Gamble If You Must: Inequalities for Stochastic Processes. McGraw Hill, New York. 2nd edition (1976). Dover, New York.
Dubins, L., Maitra, A., Purves, R. and Sudderth, W. (1989). Measurable, nonleavable gambling problems. Israel J. Math. 67 257–271.
Maitra, A. and Sudderth, W. (1992). An operator solution of stochastic games. Israel J. Math. 78 33–49.
Maitra, A. and Sudderth, W. (1993). Borel stochastic games with limsup payoff. Annals Prob. 21 861–865.
Maitra, A. and Sudderth, W. (1993). Finitely additive and measurable stochastic games. Intl. J. Game Theor. 22 201–223.
Maitra, A. and Sudderth, W. (1996). Discrete Gambling and Stochastic Games, Springer-Verlag, NY.
Mertens, J.-F. and Neyman, A. (1981). Stochastic games. Intl. J. of Game Theor. 10 53–66.
Milnor, J. and Shapley, L.S. (1957). On games of survival. Contributions to the Theory of Games,by M. Dresher, A.W. Tucker, and P. Wolfe, Eds., Ann. Math. Study No. 39, Princeton University Press, Princeton.
Nowak, A.S. (1985). Universally measurable strategies in zero-sum stochastic games. Ann. Prob. 13 269–287.
Strauch, R.E. (1966). Negative dynamic programming. Ann. Math. Statist. 37 871–890.
Strauch, R.E. (1967). Measurable gambling houses. Transac. of the Am. Math. Soc. 126 64–72.
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Maitra, A., Sudderth, W. (1999). An Introduction to Gambling Theory and Its Applications to Stochastic Games. In: Bardi, M., Raghavan, T.E.S., Parthasarathy, T. (eds) Stochastic and Differential Games. Annals of the International Society of Dynamic Games, vol 4. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1592-9_5
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DOI: https://doi.org/10.1007/978-1-4612-1592-9_5
Publisher Name: Birkhäuser, Boston, MA
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