Abstract
Mixed strategy ∈-equilibrium points are given forN-person games with cost functions consisting of quadratic, bilinear, and linear terms and strategy spaces consisting of closed balls in Hilbert spaces. The results are applied to linear-quadratic differential games with no information and quadratic integral constraints on the control functions.
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References
Wilson, D. J.,Mixed Strategy Solutions for Quadratic Games, Journal of Optimization Theory and Applications, Vol. 13, pp. 319–333, 1974.
Scalzo, R. C.,N-person Linear-Quadratic Differential Games with Constraints, SIAM Journal on Control, Vol. 12, pp. 419–425, 1974.
Halmos, P. R.,A Hilbert Space Problem Book, Springer-Verlag, New York, New York, 1974.
Vidyasagar, M.,A New Approach to N-person, Nonzero-Sum, Linear Differential Games, Journal of Optimization Theory and Applications, Vol. 18, pp. 171–175, 1976.
Dunford, N., andSchwartz, J. T.,Linear Operators, Part 1, John Wiley and Sons (Interscience Publishers), New York, New York, 1957.
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Communicated by G. Leitmann
This work was supported by a Commonwealth of Australia, Postgraduate Research Award.
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Williams, R.J. Mixed strategy solutions forN-person quadratic games. J Optim Theory Appl 30, 569–582 (1980). https://doi.org/10.1007/BF01686721
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DOI: https://doi.org/10.1007/BF01686721