Abstract
The uniqueness of Nash equilibria is shown for a class of stochastic differential games where the dynamic constraints are linear in the control variables. The result is applied to an oligopoly.
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References
Basar, R.,Informationally Nonunique Equilibrium Solutions in Differential Games, SIAM Journal on Control and Optimization, Vol. 15, pp. 636–660, 1977.
Basar, T., andOlsder, G. J.,Dynamic Noncooperative Game Theory, Academic Press, New York, New York, 1982.
Papavassilopoulos, G. P., andCruz, J. B., Jr.,On the Uniqueness of Nash Strategies for a Class of Analytic Differential Games, Journal of Optimization Theory and Applications, Vol. 27, pp. 309–314, 1979.
Uchida, K.,On the Existence of a Nash Equilibrium Point in N-Person, Nonzero-Sum Stochastic Differential Games, SIAM Journal on Control and Optimization, Vol. 16, pp. 142–149, 1978.
Ladyzenskaja, O. A., Solonnikov, V. A., andUral'ceva, N. N.,Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, Rhode Island, 1968.
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Communicated by G. Leitmann
This paper benefitted from comments by two anonymous referees and by L. Blume and C. Simon.
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Wernerfelt, B. Uniqueness of Nash equilibrium for linear-convex stochastic differential games. J Optim Theory Appl 53, 133–138 (1987). https://doi.org/10.1007/BF00938822
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DOI: https://doi.org/10.1007/BF00938822