Proceedings of the 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)

Penalty Game with Mission Success Rates and Randomizing Mixed Nash Equilibrium Strategies-Based on Monte Carlo Simulation

Authors
Yicheng Gong, Xiaomeng Niu, Jingjing Yuan, Juan Zhao, Yanna Zhang
Corresponding Author
Yicheng Gong
Available Online March 2017.
DOI
https://doi.org/10.2991/msam-17.2017.14How to use a DOI?
Keywords
game theory; penalty game; mixed Nash equilibrium; strategy; Monte Carlo simulation
Abstract
This article aims at improving the practice feasibility of game theory for the couches and athletes in a football penalty game. Firstly, some mission success rates are introduced to the penalty game to depict the technical uncertainty. Secondly, direction strategies are digitalized in order to be randomized later by Matlab. Lastly, Monte Carlo(MC) simulation is adopted to randomize the players' direction strategies, according to the probability distribution of a mixed Nash equilibrium. On the statistical data, taking Messi and Dalei Wang as an imaginary example of penalty game, the mixed equilibrium distribution is ((0.193, 0.065, 0.741); (0.035,0.0262,0.703)). Theoretically, Messi is expected to selects the left, middle and right direction as the probability 0.193, 0.065 and 0.741 respectively; and Dalei Wang is expected to selects the left, middle and right direction as the probability 0.035,0.0262 and 0.703 respectively. The simulation results show that the randomizing coincides with the probability distribution of Nash equilibrium above 91%.
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Proceedings
2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)
Part of series
Advances in Intelligent Systems Research
Publication Date
March 2017
ISBN
978-94-6252-324-1
ISSN
1951-6851
DOI
https://doi.org/10.2991/msam-17.2017.14How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Yicheng Gong
AU  - Xiaomeng Niu
AU  - Jingjing Yuan
AU  - Juan Zhao
AU  - Yanna Zhang
PY  - 2017/03
DA  - 2017/03
TI  - Penalty Game with Mission Success Rates and Randomizing Mixed Nash Equilibrium Strategies-Based on Monte Carlo Simulation
BT  - 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)
PB  - Atlantis Press
SP  - 53
EP  - 56
SN  - 1951-6851
UR  - https://doi.org/10.2991/msam-17.2017.14
DO  - https://doi.org/10.2991/msam-17.2017.14
ID  - Gong2017/03
ER  -