Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2017-09-01

Journal: IET CONTROL THEORY AND APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 11

Issue: 13,SI

Page Number: 2146-2151

ISSN: 1751-8644

Key Words: set theory; search problems; tensors; matrix multiplication; game theory; polytope strategy sets; discrete time linear dynamic games; finite horizon payoff functions; semitensor matrix product; searching Nash equilibrium problem; finite game problem

Abstract: This brief investigates the discrete time, linear dynamic games with finite horizon payoff functions. By resorting to the semi-tensor product of matrices, the authors prove that the linear dynamic game is a potential game. Then, they confine their attention to a special case: the strategy sets of game are polytopes. In this case, the searching Nash equilibrium problem for the linear dynamic game converts into one for a finite game. Furthermore, two different algorithms are designed for searching Nash equilibrium. Finally, an example is employed to validate the proposed algorithms.