Abstract
In this work we extend the work of Rosen [9] for convex finite dimensional games to a dynamic setting described by a family of abstract control problems. In particular we define the notion of a normalized Nash equilibrium and provide conditions for existence and uniqueness as well as providing necessary conditions.
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References
H.F. Bohnenblust and S. Karlin, On a theorem of Ville, Contributions to the Theory of Games, Vol. 1 (H. W. Kuhn and A. W. Tucker, eds.), Princeton University Press, Princeton, New Jersey, 1950, pp. 155–160.
D.A. Carlson, Open Loop Nash-equilibrium for Nonlinear Control Systems,System Modeling and Optimization (Polis, Michael; Dontchev, Asen L; Kall, Peter; Lasiecka, Irena; Olbrot, Andrew W, ed.), CRC Press, 1999.
D.A. Carlson and Haurie A., Infinite horizon dynamic games with coupled state constraints,to appear in Annals of the International Society of Dynamic Games, 1998.
D.A. Carlson and A. Haurie, A turnpike theory for infinite horizon open-loop differential games with decoupled controls,New Trends in Dynamic Games and Applications (G. J. Olsder, ed.), Annals of the International Society of Dynamic Games, Birkhäuser, Boston, 1995, pp. 353–376.
D.A. Carlson and A. Haurie, A turnpike theory for infinite horizon open-loop competitive processes,SIAM Journal on Control and Optimization 34 (1996), no. 4, 1405–1419.
D.A. Carlson, Existence and uniqueness in convex games with strategies in Hilbert spaces,Annals of the International Society of Dynamic Games (E. Altman and O. Pourtallier, eds), Birkhäuser, Boston, 2001.
B.D. Craven, Mathematical programming and control theory, Chapman and Hall Ltd., London, 1978.
D.G. Luenberger, Optimization by vector space methods, John Wiley and Sons, Inc., New York, NY, 1969.
J.B. Rosen, Existence and uniqueness of equilibrium points for concave n-person games, Econometrica 33 (1965), no. 3, 520–534.
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Carlson, D.A. (2002). Uniqueness of Normalized Nash Equilibrium for a Class of Games With Strategies in Banach Spaces. In: Zaccour, G. (eds) Decision & Control in Management Science. Advances in Computational Management Science, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3561-1_18
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DOI: https://doi.org/10.1007/978-1-4757-3561-1_18
Publisher Name: Springer, Boston, MA
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