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Indexed by:期刊论文

Date of Publication:2017-09-01

Journal:IET CONTROL THEORY AND APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:11

Issue:13,SI

Page Number:2146-2151

ISSN No.: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.