On the Time Consistency of Equilibria in a Class of Additively separable Differential Games

• Published in: Journal of optimization theory and applications Vol. 145; no. 3; pp. 415 - 427
• Main Authors: Bacchiega, E., Lambertini, L., Palestini, A.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-06-2010; Springer; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied sciences; Calculus of Variations and Optimal Control; Optimization; Decision theory. Utility theory; Engineering; Equilibrium; Exact sciences and technology; Feedback; Game theory; Mathematical programming; Mathematics; Mathematics and Statistics; Operational research and scientific management; Operational research. Management science; Operations Research/Decision Theory; Optimization; Studies; Theory of Computation; Additive separability; Time consistency; Differential games; Nash strategy; Partition; Separability; Decision making; Redundancy; Feedback regulation; Two person game; Game theory; Stackelberg strategy; Feedback; Preference; Open loop; Game equilibrium; Differential game; Temporal coherence; Payoff function
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-010-9673-6

A class of state-redundant differential games is detected, where players can be partitioned into two groups, so that the state dynamics and the payoff functions of all players are additively separable w.r.t. controls and states of any two players belonging to different groups. We prove that, in this class of games, open-loop Nash and feedback Stackelberg equilibria coincide, both being strongly time consistent. This allows us to bypass the issue of the time inconsistency that typically affects the open-loop Stackelberg solution.