Abstract
Linear closed-loop no-memory strategies for the LQ Nash game are considered. We exhibit a class of such problems with the property that the solution exists for any finite time interval; for the infinite time case, there exist none or a unique or many solutions, depending on the choice of the parameters. In addition, the limit of the finite time solution as the time interval increases does not have to yield the infinite time case solution. A geometric formulation of the coupled algebraic Riccati equation is given. This formulation seems to be an interesting starting point for a thorough study of these equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Basar, T., andOlsder, G. J.,Dynamic Noncooperative Game Theory, Academic Press, New York, New York, 1982.
Mageirou, E.,Values and Strategies for Infinite-Time, Linear-Quadratic Games, IEEE Transactions on Automatic Control, Vol. AC-21, pp. 547–550, 1976.
Potter, J. E.,Matrix Quadratic Solutions, SIAM Journal on Applied Mathematics, Vol. 14, pp. 496–501, 1966.
Martensson, K.,On the Matrix Riccati Equations, Information Sciences, Vol. 3, pp. 17–49, 1971.
Author information
Authors and Affiliations
Additional information
Communicated by Y. C. Ho
This work was supported in part by the United States Air Force, Office of Scientific Research, under Grants Nos. AFOSR-80-0171 and AFOSR-82-0174.
Rights and permissions
About this article
Cite this article
Papavassilopoulos, G.P., Olsder, G.J. On the linear-quadratic, closed-loop, no-memory Nash game. J Optim Theory Appl 42, 551–560 (1984). https://doi.org/10.1007/BF00934566
Issue Date:
DOI: https://doi.org/10.1007/BF00934566