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Mathematical Problems in Engineering
Volume 2014, Article ID 640960, 8 pages
http://dx.doi.org/10.1155/2014/640960
Research Article

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

1Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China
2Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong
3Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway
4School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia

Received 19 January 2014; Accepted 3 March 2014; Published 8 April 2014

Academic Editor: Michael Lütjen

Copyright © 2014 Zhengtian Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 -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.