A mixed 0-1 linear programming approach to the computation of all pure-strategy nash equilibria of a finite n -person game in normal form
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Original versionWu, Z., Dang, C., Karimi, H. R., Zhu, C., & Gao, Q. (2014). A mixed 0-1 linear programming approach to the computation of all pure-strategy nash equilibria of a finite n -person game in normal form. Mathematical Problems in Engineering, 2014. doi: 10.1155/2014/640960 10.1155/2014/640960
A main concern in applications of game theory is how to effectively select a Nash equilibrium, especially a pure-strategy Nash equilibrium for a finite n -person game in normal form. This selection process often requires the computation of all Nash equilibria. It is well known that determining whether a finite game has a pure-strategy Nash equilibrium is an NP-hard problem and it is difficult to solve by naive enumeration algorithms. By exploiting the properties of pure strategy and multilinear terms in the payoff functions, this paper formulates a new mixed 0-1 linear program for computing all pure-strategy Nash equilibria. To our knowledge, it is the first method to formulate a mixed 0-1 linear programming for pure-strategy Nash equilibria and it may work well for similar problems. Numerical results show that the approach is effective and this method can be easily distributed in a distributed way. © 2014 Zhengtian Wu et al.
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2014/640960