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

DOI

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%.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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  - Proceedings of the 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  - 10.2991/msam-17.2017.14
ID  - Gong2017/03
ER  -