Extensive Game of Horse Race: A Research on <i>Tian Ji's Horse Race</i> Based on Static Games of Complete Information

Lun Weicheng

doi:doi:10.11648/j.si.20170506.21

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Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information

Lun Weicheng

Published in Science Innovation (Volume 5, Issue 6)

Received: 5 December 2017 Published: 6 December 2017

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Abstract

There are many ways to develop of the classical problem about Tian Ji's Horse Race so that this problem may be researched deeply using theory of games. Therefore, this paper designs n-order extensive game of horse race by changing a rule of traditional problem. After analysis, this paper holds a belief that this game is a kind of static games of complete information, which means theory of static games of complete information can be used to research Tian Ji's Horse Race. With showing all of the strategy profiles of third-order extensive game of horse race and calculating Nash equilibrium of this game, this paper finds some characteristics of the strategy profiles and Nash equilibrium of extensive game of horse race and give the expression of Nash equilibrium of mixed strategy of this game. A new concept of layout is introduced to reveal how strategy profiles influence the outcome of this game. Then the characteristic of the layouts of extensive game of horse race and the layout that can make Tian Ji’s payoff biggest are found and proved, which is drawn from the result of some simulations about fourth-order and fifth-rank extensive games of horse race using a Java program.

Published in	Science Innovation (Volume 5, Issue 6)
DOI	10.11648/j.si.20170506.21
Page(s)	392-397
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Static Games of Complete Information, Strategy Profile, Nash Equilibrium, Layout

References

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[4]	柯政.“选考”制度下的“田忌赛马”：原因与对策[J].教育发展研究，2011,18:32-38。
[5]	刘祖华，冯爱芳.用Mathematicia软件求解矩阵博弈[J].高度数学研究，2017,20(4):71-74。
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[7]	史蒂文·泰迪里斯.博弈论导论[M].李井奎，北京：中国人民大学出版社，2015:60-61。
[8]	蒋志芳.对“齐王赛马”问题的求解.南京经济学院学报，2002,1:34-36。
[9]	周瀚光.论孙膑的对策论和辩证法[J].齐鲁学刊，1984,3:36-39。
[10]	范如国.博弈论[M].武汉：武汉大学出版社，2011:10-11。
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Lun Weicheng. (2017). Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information. Science Innovation, 5(6), 392-397. https://doi.org/10.11648/j.si.20170506.21

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ACS Style

Lun Weicheng. Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information. Sci. Innov. 2017, 5(6), 392-397. doi: 10.11648/j.si.20170506.21

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AMA Style

Lun Weicheng. Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information. Sci Innov. 2017;5(6):392-397. doi: 10.11648/j.si.20170506.21

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@article{10.11648/j.si.20170506.21,
  author = {Lun Weicheng},
  title = {Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information},
  journal = {Science Innovation},
  volume = {5},
  number = {6},
  pages = {392-397},
  doi = {10.11648/j.si.20170506.21},
  url = {https://doi.org/10.11648/j.si.20170506.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.si.20170506.21},
  abstract = {There are many ways to develop of the classical problem about Tian Ji's Horse Race so that this problem may be researched deeply using theory of games. Therefore, this paper designs n-order extensive game of horse race by changing a rule of traditional problem. After analysis, this paper holds a belief that this game is a kind of static games of complete information, which means theory of static games of complete information can be used to research Tian Ji's Horse Race. With showing all of the strategy profiles of third-order extensive game of horse race and calculating Nash equilibrium of this game, this paper finds some characteristics of the strategy profiles and Nash equilibrium of extensive game of horse race and give the expression of Nash equilibrium of mixed strategy of this game. A new concept of layout is introduced to reveal how strategy profiles influence the outcome of this game. Then the characteristic of the layouts of extensive game of horse race and the layout that can make Tian Ji’s payoff biggest are found and proved, which is drawn from the result of some simulations about fourth-order and fifth-rank extensive games of horse race using a Java program.},
 year = {2017}
}

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TY  - JOUR
T1  - Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information
AU  - Lun Weicheng
Y1  - 2017/12/06
PY  - 2017
N1  - https://doi.org/10.11648/j.si.20170506.21
DO  - 10.11648/j.si.20170506.21
T2  - Science Innovation
JF  - Science Innovation
JO  - Science Innovation
SP  - 392
EP  - 397
PB  - Science Publishing Group
SN  - 2328-787X
UR  - https://doi.org/10.11648/j.si.20170506.21
AB  - There are many ways to develop of the classical problem about Tian Ji's Horse Race so that this problem may be researched deeply using theory of games. Therefore, this paper designs n-order extensive game of horse race by changing a rule of traditional problem. After analysis, this paper holds a belief that this game is a kind of static games of complete information, which means theory of static games of complete information can be used to research Tian Ji's Horse Race. With showing all of the strategy profiles of third-order extensive game of horse race and calculating Nash equilibrium of this game, this paper finds some characteristics of the strategy profiles and Nash equilibrium of extensive game of horse race and give the expression of Nash equilibrium of mixed strategy of this game. A new concept of layout is introduced to reveal how strategy profiles influence the outcome of this game. Then the characteristic of the layouts of extensive game of horse race and the layout that can make Tian Ji’s payoff biggest are found and proved, which is drawn from the result of some simulations about fourth-order and fifth-rank extensive games of horse race using a Java program.
VL  - 5
IS  - 6
ER  -

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Author Information

Lun Weicheng

College of Systems Engineering, National University of Defense Technology, Changsha, China

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APA Style

Lun Weicheng. (2017). Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information. Science Innovation, 5(6), 392-397. https://doi.org/10.11648/j.si.20170506.21

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ACS Style

Lun Weicheng. Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information. Sci. Innov. 2017, 5(6), 392-397. doi: 10.11648/j.si.20170506.21

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AMA Style

Lun Weicheng. Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information. Sci Innov. 2017;5(6):392-397. doi: 10.11648/j.si.20170506.21

Copy | Download

@article{10.11648/j.si.20170506.21,
  author = {Lun Weicheng},
  title = {Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information},
  journal = {Science Innovation},
  volume = {5},
  number = {6},
  pages = {392-397},
  doi = {10.11648/j.si.20170506.21},
  url = {https://doi.org/10.11648/j.si.20170506.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.si.20170506.21},
  abstract = {There are many ways to develop of the classical problem about Tian Ji's Horse Race so that this problem may be researched deeply using theory of games. Therefore, this paper designs n-order extensive game of horse race by changing a rule of traditional problem. After analysis, this paper holds a belief that this game is a kind of static games of complete information, which means theory of static games of complete information can be used to research Tian Ji's Horse Race. With showing all of the strategy profiles of third-order extensive game of horse race and calculating Nash equilibrium of this game, this paper finds some characteristics of the strategy profiles and Nash equilibrium of extensive game of horse race and give the expression of Nash equilibrium of mixed strategy of this game. A new concept of layout is introduced to reveal how strategy profiles influence the outcome of this game. Then the characteristic of the layouts of extensive game of horse race and the layout that can make Tian Ji’s payoff biggest are found and proved, which is drawn from the result of some simulations about fourth-order and fifth-rank extensive games of horse race using a Java program.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Extensive Game of Horse Race: A Research on Tian Ji's Horse Race Based on Static Games of Complete Information
AU  - Lun Weicheng
Y1  - 2017/12/06
PY  - 2017
N1  - https://doi.org/10.11648/j.si.20170506.21
DO  - 10.11648/j.si.20170506.21
T2  - Science Innovation
JF  - Science Innovation
JO  - Science Innovation
SP  - 392
EP  - 397
PB  - Science Publishing Group
SN  - 2328-787X
UR  - https://doi.org/10.11648/j.si.20170506.21
AB  - There are many ways to develop of the classical problem about Tian Ji's Horse Race so that this problem may be researched deeply using theory of games. Therefore, this paper designs n-order extensive game of horse race by changing a rule of traditional problem. After analysis, this paper holds a belief that this game is a kind of static games of complete information, which means theory of static games of complete information can be used to research Tian Ji's Horse Race. With showing all of the strategy profiles of third-order extensive game of horse race and calculating Nash equilibrium of this game, this paper finds some characteristics of the strategy profiles and Nash equilibrium of extensive game of horse race and give the expression of Nash equilibrium of mixed strategy of this game. A new concept of layout is introduced to reveal how strategy profiles influence the outcome of this game. Then the characteristic of the layouts of extensive game of horse race and the layout that can make Tian Ji’s payoff biggest are found and proved, which is drawn from the result of some simulations about fourth-order and fifth-rank extensive games of horse race using a Java program.
VL  - 5
IS  - 6
ER  -

Copy | Download