Penalty Game with Mission Success Rates and Randomizing Mixed Nash Equilibrium Strategies-Based on Monte Carlo Simulation
Yicheng Gong, Xiaomeng Niu, Jingjing Yuan, Juan Zhao, Yanna Zhang
Available Online March 2017.
- https://doi.org/10.2991/msam-17.2017.14How to use a DOI?
- game theory; penalty game; mixed Nash equilibrium; strategy; Monte Carlo simulation
- 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%.
- 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 -