Open AccessLinear dynamic games with polytope strategy sets
Author(s) -
Wu Yuhu,
Toyoda Mitsuru,
Shen Tielong
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.1667
Subject(s) - polytope , sequential game , nash equilibrium , stochastic game , mathematical optimization , best response , normal form game , computer science , symmetric game , strategy , repeated game , game theory , mathematics , mathematical economics , discrete mathematics
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.