Abstract
In this paper, we consider scalar linear stochastic differential games with average cost criterions. We solve the dynamic programming equations for these games and give the synthesis of saddle-point and Nash equilibrium solutions.
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References
Başar, T., andOlsder, G. J.,Dynamic Noncooperative Game Theory, Academic Press, London, England, 1982.
Kumar, P. R., andVaraiya, P.,Stochastic Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1986.
Da Prato, G., andIchikawa, A.,Quadratic Control for Linear Periodic Systems, Applied Mathematics and Optimization, Vol. 18, pp. 39–66, 1988.
Veretennikov, A. Yu.,On Strong Solutions and Explicit Formulas for Solutions of Stochastic Integral Equations, Mathematics of the USSR Sbornik, Vol. 39, pp. 387–403, 1981.
Fujita, Y., andMorimoto, H.,On Bang-Bang Solutions of Stochastic Differential Games, IEEE Transactions on Automatic Control, Vol. AC-32, pp. 535–537, 1987.
Liptser, R. S. A Strong Law of Large Numbers for Local Martingales, Stochastics, Vol. 3, pp. 217–228, 1980.
Bensoussan, A.,Stochastic Control by Functional Analysis Methods, North-Holland, Amsterdam, Holland, 1982.
Fleming, W. H., andRishel, R. W.,Deterministic and Stochastic Optimal Control, Springer-Verlag, New York, New York, 1975.
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Communicated by P. Varaiya
The authors wish to thank A. Ichikawa for providing the initial impetus and helpful advice.
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Morimoto, H., Ohashi, M. On linear stochastic differential games with average cost criterions. J Optim Theory Appl 64, 127–140 (1990). https://doi.org/10.1007/BF00940027
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DOI: https://doi.org/10.1007/BF00940027