Design of zero-determinant strategies and its application to networked repeated games  

作　　者：Daizhan CHENG Changxi LI 

机构地区：[1]Key Laboratory of Systems and Control,Academy of Mathematics and Systems Sciences,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Science China(Information Sciences)》2024年第10期223-239,共17页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.62103232,62073315,62350037);Natural Science Fund of Shandong Province(Grant No.ZR2021QF005);Taishan Scholar Project of Shandong Province(Grant No.tsqn202312033)。

摘　　要：Using the semi-tensor product(STP)of matrices,the profile evolutionary equation(PEE)for repeated finite games is obtained.By PEE,the zero-determinant(ZD)strategies are developed for general finite games.A formula is then obtained to design ZD strategies for general finite games with multiple players and asymmetric strategies.A necessary and sufficient condition is obtained to ensure the availability of the designed ZD strategies.It follows that player i can unilaterally design k_i-1(one less than the number of its strategies)dominating linear relations about the expected payoffs of all players.Finally,the fictitious opponent player is proposed for networked repeated games(NRGs).A technique is proposed to simplify the model by reducing the number of frontier strategies.

关 键 词：finite repeated game profile evolutionary equation ZD strategy networked repeated games semi-tensor product of matrices 

分 类 号：O225[理学—运筹学与控制论]