Semi-tensor product approach to networked evolutionary games

作     者：Daizhan CHENG Hongsheng QI Fehuang HE Tingting XU Hairong DONG 

作者机构：Ins titu te of Systems Science Chinese Academy of Sciences Beijing 100190 China Institute of Astronautics Harbin Institute of Technology Harbin Heilongjiang 150080 China State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing 100044 China 

出 版 物：《Control Theory and Technology》 (控制理论与技术（英文版）)

年 卷 期：2014年第12卷第2期

页      面：198-214页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 081202[工学-计算机软件与理论] 

基　　金：This work was partially supported by National Natural Science Foundation of China (Nos. 61273013  61333001  61104065  61322307) 

主　　题：Networked evolutionary game Fundamental evolutionary equation Strategy profile dynamics Homogeneous/heterogeneous NEG Semi-tensor product of matrices 

摘      要：In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.