Abstract
It is a main concern in applications of game theory to effectively select a Nash equilibrium. All Nash equilibria is often required to be computed for this selection process. However, it is well known that the problem of finding only one mixed-strategy Nash equilibrium is a PPAD-complete process. Therefore, it is very hard to find all Nash equilibrium for a certain problem by traditional methods. By exploiting the properties of multilinear terms in the payoff functions, this paper presents a good approximation of the multilinear terms and develops a mixed-integer linear programming for finding all mixed-strategy Nash equilibria. An example of this method will be given too.
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Acknowledgement
This work was partially supported by GRF(CityU 112910 of Hong Kong SAR Government), ARG(CityU 9667080 of Hong Kong SAR Government), the National Natural Science Foundation of China under Grant No.61472267 and Nature Foundation of Jiangsu Province under Grant No.BK2012166.
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Wu, Z., Dang, C., Hu, F., Fu, B. (2015). A New Method to Finding All Nash Equilibria. In: He, X., et al. Intelligence Science and Big Data Engineering. Big Data and Machine Learning Techniques. IScIDE 2015. Lecture Notes in Computer Science(), vol 9243. Springer, Cham. https://doi.org/10.1007/978-3-319-23862-3_49
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DOI: https://doi.org/10.1007/978-3-319-23862-3_49
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