Games are an ideal vehicle for showcasing the crucial role information plays in decision systems. Indeed, game theory plays a major role in economic theory, and, in particular, in microeconomic theory—one aptly refers to information economics. The role of information is further amplified in dynamic games. One then refers to the information pattern of the game. In this paper nonzero-sum differential games are addressed and open-loop and state feedback information patterns are considered. Nash equilibria (NE) when complete state information is available and feedback strategies are sought are compared to open-loop NE. In contrast to optimal control and, remarkably, zero-sum differential games, in nonzero-sum differential games the optimal trajectory and the players’ values when closed-loop strategies are used are not the same as when open-loop strategies are used. This is amply illustrated in the special case of nonzero-sum Linear-Quadratic differential games. Results which quantify the cost of uncertainty are derived and insight into the dynamics of information systems is obtained.
[1]
B. Wie.
A differential game approach to the dynamic mixed behavior traffic network equilibrium problem
,
1995
.
[2]
J. Case,et al.
Toward a theory of many player differential games.
,
1969
.
[3]
Y. Ho,et al.
Nonzero-sum differential games
,
1969
.
[4]
T. Başar,et al.
Dynamic Noncooperative Game Theory, 2nd Edition
,
1998
.
[5]
James H. Case.
Equilibrium points of N-person differential games
,
1967
.
[6]
Y. Ho,et al.
Further properties of nonzero-sum differential games
,
1969
.
[7]
Geert Jan Olsder,et al.
On Open- and Closed-Loop Bang-Bang Control in Nonzero-Sum Differential Games
,
2001,
SIAM J. Control. Optim..
[8]
Jacob Engwerda,et al.
LQ Dynamic Optimization and Differential Games
,
2005
.
[9]
T. Başar,et al.
Dynamic Noncooperative Game Theory
,
1982
.
[10]
Byung-Wook Wie,et al.
A differential game model of Nash equilibrium on a congested traffic network
,
1993,
Networks.