Decision-implementation complexity of cooperative game systems  

作　　者：Changbao XU Yanlong ZHAO Ji-Feng ZHANG 

机构地区：[1]Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science,Chinese Academy of Sciences [2]School of Mathematical Sciences, University of Chinese Academy of Sciences

出　　处：《Science China(Information Sciences)》2017年第11期176-193,共18页中国科学（信息科学）（英文版）

基　　金：supported by National Basic Research Program of China (973 Program) (Grant No. 2014CB845301);National Natural Science Foundation of China (Grant No. 61227902)

摘　　要：This paper focuses on the decision-implementation complexity （DIC） of cooperative games. The complexity of a control law is a fundamental issue in practice because it is closely related to control cost. First, we formulate implementation measures of strategies as system control protocols. Then, for a class of cooperative games, a decision-implementation system model is established, and an energy-based DIG index is given as the energy expectation under Nash equilibrium strategies. A definition of DIC is presented to describe the optimal values of the DIC index. DIC is calculated by the exhaust algorithm in some specific cases, whereas the one for general cases is too complex to be calculated. In order to obtain a general calculation method, the problem is described in the form of matrices; an analytical expression describing DIC is obtained by using the properties of matrix singular values. Furthermore, when only partial information of actions is shared among players, DIC can be reduced and an improved protocol can be designed as a two-phase protocol. A numerical example is given to show that the DIC obtained in this study is the same as the one obtained by the exhaust algorithm, and that the calculation complexity of the proposed algorithm is much lower.This paper focuses on the decision-implementation complexity （DIC） of cooperative games. The complexity of a control law is a fundamental issue in practice because it is closely related to control cost. First, we formulate implementation measures of strategies as system control protocols. Then, for a class of cooperative games, a decision-implementation system model is established, and an energy-based DIG index is given as the energy expectation under Nash equilibrium strategies. A definition of DIC is presented to describe the optimal values of the DIC index. DIC is calculated by the exhaust algorithm in some specific cases, whereas the one for general cases is too complex to be calculated. In order to obtain a general calculation method, the problem is described in the form of matrices; an analytical expression describing DIC is obtained by using the properties of matrix singular values. Furthermore, when only partial information of actions is shared among players, DIC can be reduced and an improved protocol can be designed as a two-phase protocol. A numerical example is given to show that the DIC obtained in this study is the same as the one obtained by the exhaust algorithm, and that the calculation complexity of the proposed algorithm is much lower.

关 键 词：cooperative game distributed protocol optimal control decision-implementation complexity two-phase protocol 

分 类 号：O225[理学—运筹学与控制论]