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Special Issue:
TOPICAL REVIEW — Statistical Physics and Complex Systems
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| TOPICAL REVIEW—Statistical Physics and Complex Systems |
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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 |
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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.
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Received: 03 March 2014
Revised: 20 May 2014
Accepted manuscript online:
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PACS:
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89.75.Fb
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(Structures and organization in complex systems)
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02.50.Le
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(Decision theory and game theory)
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89.65.-s
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(Social and economic systems)
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| 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: zhutou@ustc.edu
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Cite this article:
Hao Dong (郝东), Rong Zhi-Hai (荣智海), Zhou Tao (周涛) Zero-determinant strategy：An underway revolution in game theory 2014 Chin. Phys. B 23 078905
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| [1] |
Axelrod R and Hamilton W D 1981 Science 211 1390
|
| [2] |
Axelrod R 1984 The Evolution of Cooperation (New York: Basic Book)
|
| [3] |
Axelrod R and Dion D 1988 Science 242 1385
|
| [4] |
Nowak M A 2006 Science 314 1560
|
| [5] |
Szabó G and Fath G 2007 Phys. Rep. 446 97
|
| [6] |
Kendall G, Yao X and Chong S Y 2007 The Iterative Prisoners' Dilemma: 20 Years On (Singapore: World Scientific)
|
| [7] |
Hardin G 1968 Science 162 1243
|
| [8] |
Mailath G and Samuelson L 2006 Repeated Games and Reputations: Long-Run Relationships (New York: Oxford University Press)
|
| [9] |
Kandori M 1992 Review of Economic Studies 59 63
|
| [10] |
Press W H and Dyson F J 2012 Proc. Acad. Natl. Sci. USA 109 10409
|
| [11] |
Stewart A J and Plotkin J B 2012 Proc. Acad. Natl. Sci. USA 109 10134
|
| [12] |
Hayes B 2013 American Scientist 101 422
|
| [13] |
Akin E 2012 arXiv:1211.0969 [math.DS]
|
| [14] |
Chen J and Zinger A (unpublished)
|
| [15] |
Adami C and Hintze A 2013 Nat. Commun. 4 3193
|
| [16] |
Hilbe C, Nowak M A and Sigmund K 2013 Proc. Acad. Natl. Sci. USA 110 6913
|
| [17] |
Roemheld L 2013 arXiv:1308.2576 [cs.GT]
|
| [18] |
Stewart A J and Plotkin J B 2013 Proc. Acad. Natl. Sci. USA 110 15348
|
| [19] |
Hilbe C, Nowak M A and Traulsen A 2013 PLoS ONE 8 e77886
|
| [20] |
Neumann J V and Morgenstern O 1944 Theory of Games and Economic Behavior (Princeton: Princeton University Press)
|
| [21] |
Nash J F 1950 Proc. Acad. Natl. Sci. USA 36 48
|
| [22] |
Nowak M A and Sigmund K 1992 Nature 355 250
|
| [23] |
Nowak M A and Sigmund K 1993 Nature 364 56
|
| [24] |
Smith J M 1982 Evolution and the Theory of Games (Cambridge: Cambridge University Press)
|
| [25] |
Nowak M A, Sasaki A, Taylor C and Fudenberg D 2004 Nature 428 646
|
| [26] |
Szolnoki A and Perc M 2014 Phys. Rev. E 89 022804
|
| [27] |
Pan L, Hao D, Rong Z and Zhou T 2014 arXiv:1402.3542 [cs.GT]
|
| [28] |
Hilbe C, Traulsen A, Wu B and Nowak M A 2014 arXiv:1404.2886 [q-bio.PE]
|
| [29] |
Hao D, Rong Z, Pan L and Zhou T (unpublished)
|
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