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Chin. Phys. B, 2014, Vol. 23(7): 078905    DOI: 10.1088/1674-1056/23/7/078905
Special Issue: TOPICAL REVIEW — Statistical Physics and Complex Systems
TOPICAL REVIEW—Statistical Physics and Complex Systems Prev   Next  

Zero-determinant strategy:An underway revolution in game theory

Hao Dong, Rong Zhi-Hai, Zhou Tao
Evolutionary Game Institute, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China
Abstract  Repeated games describe situations where players interact with each other in a dynamic pattern and make decisions according to outcomes of previous stage games. Very recently, Press and Dyson have revealed a new class of zero-determinant (ZD) strategies for the repeated games, which can enforce a fixed linear relationship between expected payoffs of two players, indicating that a smart player can control her unwitting co-player's payoff in a unilateral way [Proc. Acad. Natl. Sci. USA 109, 10409 (2012)]. The theory of ZD strategies provides a novel viewpoint to depict interactions among players, and fundamentally changes the research paradigm of game theory. In this brief survey, we first introduce the mathematical framework of ZD strategies, and review the properties and constrains of two specifications of ZD strategies, called pinning strategies and extortion strategies. Then we review some representative research progresses, including robustness analysis, cooperative ZD strategy analysis, and evolutionary stability analysis. Finally, we discuss some significant extensions to ZD strategies, including the multi-player ZD strategies, and ZD strategies under noise. Challenges in related research fields are also listed.
Keywords:  zero-determinant strategy      prisoner’s dilemma      evolution of cooperation      repeated game  
Received:  03 March 2014      Revised:  20 May 2014      Published:  15 July 2014
PACS:  89.75.Fb (Structures and organization in complex systems)  
  02.50.Le (Decision theory and game theory)  
  89.65.-s (Social and economic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61004098 and 11222543), the Program for New Century Excellent Talents in Universities of China (Grant No. NCET-11-0070), the Special Project of Youth Science and Technology Innovation Research Team of Sichuan Province, China (Grant No. 2013TD0006), and the Research Foundation of UESTC and Scholars Program of Hong Kong (Grant No. G-YZ4D).
Corresponding Authors:  Zhou Tao     E-mail:

Cite this article: 

Hao Dong, Rong Zhi-Hai, Zhou Tao Zero-determinant strategy:An underway revolution in game theory 2014 Chin. Phys. B 23 078905

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