TY - JOUR
T1 - Iterative computation of nash equilibria in M-player games with partial weak coupling
AU - Basar, Tamer
AU - Srikant, R.
N1 - Acknowledgement--This work was supported in part by the U.S. Department of Energy under Grant DE-FG-02-88-ER-13939.
PY - 1991
Y1 - 1991
N2 - We formulate two general classes of M-player deterministic and stochastic nonzero-sum games where the players can be placed into two groups such that there are strong interactions within each group and a weak interaction between the two groups. This weak interaction is characterized in terms of a small parameter ε which, when set equal to zero, leads to two independent nonzero-sum games. Under the Nash equilibrium solution concept both within and in between the groups, we study the merits of an iterative method for the construction of the equilibrium by solving simpler problems at each stage of the iteration. In this iterative scheme, the zero'th order solution is the Nash equilibrium of the two independent games obtained by setting ε = 0, whereas the higher-order solutions are Nash equilibria of quadratic games, even though the original problem may have non-quadratic cost functions.
AB - We formulate two general classes of M-player deterministic and stochastic nonzero-sum games where the players can be placed into two groups such that there are strong interactions within each group and a weak interaction between the two groups. This weak interaction is characterized in terms of a small parameter ε which, when set equal to zero, leads to two independent nonzero-sum games. Under the Nash equilibrium solution concept both within and in between the groups, we study the merits of an iterative method for the construction of the equilibrium by solving simpler problems at each stage of the iteration. In this iterative scheme, the zero'th order solution is the Nash equilibrium of the two independent games obtained by setting ε = 0, whereas the higher-order solutions are Nash equilibria of quadratic games, even though the original problem may have non-quadratic cost functions.
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U2 - 10.1007/bfb0040245
DO - 10.1007/bfb0040245
M3 - Conference article
AN - SCOPUS:0025794719
SN - 0170-8643
VL - 156
SP - 245
EP - 256
JO - Lecture Notes in Control and Information Sciences
JF - Lecture Notes in Control and Information Sciences
T2 - Proceedings of the 4th International Symposium on Differential Games and Applications
Y2 - 9 August 1990 through 10 August 1990
ER -