Abstract
It has been shown that two-person zero-sum separable games are associated with a maximization problem involving the cones and dual cones of the generalized moments of the players' mixed strategy sets. In this note it is observed that those results extend almost immediately to two-person nonzero-sum separable games, but that then-person extension does not follow except in a special case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Dresher and S. Karlin and L.S. Shapley, “Polynomial Games”, in: H.W. Kuhn and A.W. Tucker, eds., Contributions to the theory of games, Vol. I (Princeton University Press, Princeton, N.J., 1950) pp.161–180.
D. Gale and O. Gross, “A note on polynomial and separable games”, Pacific Journal of Mathematics 8 (1958) 735–741.
L.C. Westphal and A.R. Stubberud, “The associated maximization problem for separable games”, Mathematical Programming 5 (1973) 374–380.
M. Dresher and S. Karlin, “Solutions of convex games as fixed points”, H.W. Kuhn and A.W. Tucker, eds., Contributions to the theory of games, Vol. II (Princeton University Press, Princeton, N.J., 1953) pp. 75–86.
H. Nikaido and K. Isoda, “Note on noncooperative convex games”, Pacific Journal of Mathematics 5 (1955) 807–815.
S. Karlin and L.S. Shapley, “Geometry of moment spaces,” Memoirs of the American Mathematical Society 12 (1953).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Westphal, L.C. An associated maximization problem for two-person nonzero-sum separable games. Mathematical Programming 10, 124–129 (1976). https://doi.org/10.1007/BF01580657
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01580657