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论文类型：期刊论文

发表时间：2017-09-01

发表刊物：IET CONTROL THEORY AND APPLICATIONS

收录刊物：SCIE、EI、Scopus

卷号：11

期号：13,SI

页面范围：2146-2151

ISSN号：1751-8644

关键字：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

摘要：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.