Zero-determinant strategy：An underway revolution in game theory

doi:10.1088/1674-1056/23/7/078905

中国物理B ›› 2014, Vol. 23 ›› Issue (7): 78905-078905.doi: 10.1088/1674-1056/23/7/078905

所属专题： TOPICAL REVIEW — Statistical Physics and Complex Systems

• TOPICAL REVIEW—Statistical Physics and Complex Systems • 上一篇下一篇

Zero-determinant strategy：An underway revolution in game theory

郝东, 荣智海, 周涛

Evolutionary Game Institute, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China

收稿日期:2014-03-03 修回日期:2014-05-20 出版日期:2014-07-15 发布日期:2014-07-15
基金资助:
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).

Zero-determinant strategy：An underway revolution in game theory

Hao Dong (郝东), Rong Zhi-Hai (荣智海), Zhou Tao (周涛)

Evolutionary Game Institute, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China

Received:2014-03-03 Revised:2014-05-20 Online:2014-07-15 Published:2014-07-15
Contact: Zhou Tao E-mail:zhutou@ustc.edu
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: zero-determinant strategy, prisoner’, s dilemma, evolution of cooperation, repeated game

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.

Key words: zero-determinant strategy, prisoner’s dilemma, evolution of cooperation, repeated game

中图分类号: (Structures and organization in complex systems)

89.75.Fb

02.50.Le (Decision theory and game theory) 89.65.-s (Social and economic systems)

郝东, 荣智海, 周涛. Zero-determinant strategy：An underway revolution in game theory[J]. 中国物理B, 2014, 23(7): 78905-078905.

Hao Dong (郝东), Rong Zhi-Hai (荣智海), Zhou Tao (周涛). Zero-determinant strategy：An underway revolution in game theory[J]. Chin. Phys. B, 2014, 23(7): 78905-078905.

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Zero-determinant strategy：An underway revolution in game theory

Zero-determinant strategy：An underway revolution in game theory

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