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A Class of General Transformation of Characteristic Functions in Dynamic Games

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Abstract

The transformation of characteristic functions is an effective way to avoid time-inconsistency of cooperative solutions in dynamic games. There are several forms on the transformation of characteristic functions. In this paper, a class of general transformation of characteristic functions is proposed. It can lead to the time-consistency of cooperative solutions and guarantee that the irrational-behavior-proof conditions hold true. To illustrate the theory, an example of dynamic game on a tree is given.

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References

  1. Petrosyan L A, Stable solution of differential game with many participants, Viestnik of Leniversity University, 1977, 19: 46–52.

    Google Scholar 

  2. Petrosyan L A and Danilov N N, Consistent solutions of non-zero sum differential game with transferable utilities, Viestnik of Leniversity University, 1979, 1: 46–54.

    Google Scholar 

  3. Zaccour G, Time consistency in cooperative differential game: A tutorial, INFOR Information Systems and Operational Research, 2008, 46(1): 81–92.

    Article  MathSciNet  Google Scholar 

  4. Wang L, Gao H W, Petrosyan L A, et al., Strategically supported cooperation in dynamic games with coalition structures, Science China-Mathematics, 2016, 59(5): 1015–1028.

    Article  MathSciNet  Google Scholar 

  5. Gao H W, Petrosyan L A, Qiao H, et al., Cooperation in two-stage games on undirected networks, Journal of Systems Science and Complexity, 2017, 30(3): 680–693.

    Article  MathSciNet  Google Scholar 

  6. Wang L, Liu C, Xue J, et al., A note on strategic stability of cooperative solutions for multistage games, Discrete Dynamics in Nature and Society, Volume 2018, Article ID 3293745, 6 pages.

  7. Yeung D W K and Petrosyan L A, Subgame Consistent Cooperation — A Comprehensive Treatise, Springer, Singapore, 2016.

    Book  Google Scholar 

  8. Parilina E and Zaccour G, Node-consistent core for games played over event trees, Automatica, 2015, 53: 304–311.

    Article  MathSciNet  Google Scholar 

  9. Petrosyan L A and Sedakov A, The subgame-consistent Shapley value for dynamic network games with shock, Dynamic Games and Applications, 2016, 6(4): 520–537.

    Article  MathSciNet  Google Scholar 

  10. Gao H W and Petrosyan L A, Dynamic Cooperative Games, Science Press, Beijing, 2009 (in Chinese).

    Google Scholar 

  11. Petrosyan L A, The Shapley value for differential games, Ann. Internat. Soc. Dynam. Games, 1995, 3: 409–417.

    MathSciNet  Google Scholar 

  12. Gao H W, Petrosyan L A, Qiao H, et al., Transformation of characteristic function in dynamic games, J. Sys. Sci. Info., 2013, 1(1): 22–37.

    Google Scholar 

  13. Petrosyan L A, Sedakov A, Sun H, et al., Convergence of strong time-consistent payment schemes in dynamic games, Appl. Math. Comput., 2017, 315: 96–112.

    MathSciNet  MATH  Google Scholar 

  14. Neumann J and Morgenstern O, Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944.

    MATH  Google Scholar 

  15. Shapley L S, Cores of convex games, International Journal of Game Theory, 1971, 1(1): 11–26.

    Article  MathSciNet  Google Scholar 

  16. Yeung D W K, An irrational-behavior-proof condition in cooperative differential games, Int. J. Game Theory Rev., 2006, 8(4): 739–744.

    Article  MathSciNet  Google Scholar 

  17. Yeung D W K, Petrosyan L A, Zhuk V, et al., The detalization of the irrational behavior proof condition, Contrib. Game Theory. Manag., 2010, 3: 431–440.

    MathSciNet  MATH  Google Scholar 

  18. Mazalov V V and Rettieva A N, Incentive conditions for rational behavior in discrete-time bioresource management problem, Doklady Math., 2010, 81(3): 399–402.

    Article  MathSciNet  Google Scholar 

  19. Ji H Q, Gao H W, Wang L, et al, An asynchronous irrational behavior proof condition for the problem of emission reduction, Appl. Math. Mech., 2017, 863: 195–200.

    Google Scholar 

  20. Liu C, Gao H W, Petrosyan O, et al., Irrational-behavior-proof conditions based on limit characteristic functions, J. Sys. Sci. Info., 2019, 7(1): 1–16.

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, China

    Cui Liu & Ying Liu

  2. School of Mathematics and Statistics, Institute of Applied Mathematics of Shandong, Qingdao University, Qingdao, 266071, China

    Hongwei Gao & Lei Wang

  3. Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg, 198504, Russia

    Ovanes Petrosian

  4. School of Automation, Qingdao University, Qingdao, 266071, China

    Lei Wang

Authors
  1. Cui Liu
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  2. Hongwei Gao
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  3. Ovanes Petrosian
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  4. Ying Liu
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  5. Lei Wang
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Corresponding author

Correspondence to Lei Wang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 71571108, China Postdoctoral Science Foundation Funded Project under Grant No. 2016M600525, Qingdao Postdoctoral Application Research Project under Grant No. 2016029.

This paper was recommended for publication by Editor WANG Shouyang.

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Liu, C., Gao, H., Petrosian, O. et al. A Class of General Transformation of Characteristic Functions in Dynamic Games. J Syst Sci Complex 33, 1997–2012 (2020). https://doi.org/10.1007/s11424-020-9069-0

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  • DOI: https://doi.org/10.1007/s11424-020-9069-0

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