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Symmetry-based decomposition of finite games

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Abstract

The symmetry-based decompositions of finite games are investigated. First, the vector space of finite games is decomposed into a symmetric subspace and an orthogonal complement of the symmetric subspace. The bases of the symmetric subspace and those of its orthogonal complement are presented. Second, the potential-based orthogonal decompositions of two-player symmetric/antisymmetric games are presented. The bases and dimensions of all dual decomposed subspaces are revealed. Finally, some properties of these decomposed subspaces are obtained.

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References

  1. Nowak M A, May R M. Evolutionary games and spatial chaos. Nature, 1992, 359: 826–829

    Article  Google Scholar 

  2. Tembine H, Altman E, El-Azouzi R, et al. Evolutionary games in wireless networks. IEEE Trans Syst Man Cybern B, 2010, 40: 634–646

    Article  Google Scholar 

  3. Santos F C, Santos M D, Pacheco J M. Social diversity promotes the emergence of cooperation in public goods games. Nature, 2008, 454: 213–216

    Article  Google Scholar 

  4. Heikkinen T. A potential game approach to distributed power control and scheduling. Comput Netw, 2006, 50: 2295–2311

    Article  Google Scholar 

  5. Marden J R, Arslan G, Shamma J S. Cooperative control and potential games. IEEE Trans Syst Man Cybern B, 2009, 39: 1393–1407

    Article  Google Scholar 

  6. Niyato D, Hossain E. A noncooperative game-theoretic framework for radio resource management in 4G heterogeneous wireless access networks. IEEE Trans Mobile Comput, 2008, 7: 332–345

    Article  Google Scholar 

  7. Arslan G, Marden J R, Shamma J S. Autonomous vehicle-target assignment: a game-theoretical formulation. J Dyn Syst Meas Control, 2007, 129: 584–596

    Article  Google Scholar 

  8. Candogan O, Menache I, Ozdaglar A, et al. Flows and decompositions of games: harmonic and potential games. Math Oper Res, 2011, 36: 474–503

    Article  MathSciNet  Google Scholar 

  9. Kalai A T, Kalai E. Cooperation and competition in strategic games with private information. In: Proceedings of the 11th ACM Conference on Electronic Commerce, Cambridge, 2010. 345–346

    Chapter  Google Scholar 

  10. Hwang S H, Rey-Bellet L. Decompositions of two player games: potential, zero-sum, and stable games. 2011. ArXiv:1106.3552

    Google Scholar 

  11. Wang Y H, Liu T, Cheng D Z. From weighted potential game to weighted harmonic game. IET Control Theory Appl, 2017, 11: 2161–2169

    Article  MathSciNet  Google Scholar 

  12. Cheng D Z, Liu T, Zhang K Z, et al. On decomposed subspaces of finite games. IEEE Trans Autom Control, 2016, 61: 3651–3656

    Article  MathSciNet  Google Scholar 

  13. Cheng D Z. On finite potential games. Automatica, 2014, 50: 1793–1801

    Article  MathSciNet  Google Scholar 

  14. Cheng D Z, Liu T. Linear representation of symmetric games. IET Control Theory Appl, 2017, 11: 3278–3287

    MathSciNet  Google Scholar 

  15. Cheng D Z, He F H, Qi H S, et al. Modeling, analysis and control of networked evolutionary games. IEEE Trans Autom Control, 2015, 60: 2402–2415

    Article  MathSciNet  Google Scholar 

  16. Nash J. Non-cooperative games. Ann Math, 1951, 54: 286–295

    Article  MathSciNet  Google Scholar 

  17. Cao Z G, Yang X G. Symmetric games revisited. 2016. https://doi.org/ssrn.com/abstract=2637225

    MATH  Google Scholar 

  18. Cheng D Z, Qi H S, Zhao Y. An Introduction to Semi-Tensor Product of Matrices and Its Applications. Singapore: World Scientific, 2012

    Book  Google Scholar 

  19. Wang Y H, Liu T, Cheng D Z. Some notes on semi-tensor product of matrices and swap matrix. J Syst Sci Math Sci, 2016, 36: 1367–1375

    MathSciNet  MATH  Google Scholar 

  20. Webb J N. Game Theory. Berlin: Springer, 2007

    MATH  Google Scholar 

  21. Li C X, Liu T, He F H, et al. On finite harmonic games. In: Proceedings of the 55th Conference on Decision and Control, Las Vegas, 2016. 7024–7029

    Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61473099, 61273013, 61333001).

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Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China

    Changxi Li & Fenghua He

  2. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    Ting Liu & Daizhan Cheng

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  1. Changxi Li
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  2. Fenghua He
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  3. Ting Liu
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  4. Daizhan Cheng
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Correspondence to Fenghua He.

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Li, C., He, F., Liu, T. et al. Symmetry-based decomposition of finite games. Sci. China Inf. Sci. 62, 12207 (2019). https://doi.org/10.1007/s11432-017-9411-0

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  • DOI: https://doi.org/10.1007/s11432-017-9411-0

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