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Game Theory
Volume 2015, Article ID 862842, 2 pages
Research Article

An Algorithm for Computing All Berge Equilibria

1Center On Stochastic Modelling, Optimization, and Statistics (COSMOS), The University of Texas at Arlington, P.O. Box 19017, Arlington, TX 76019-0017, USA
2TransSolutions, LLC., 14600 Trinity Boulevard, Fort Worth, TX 76155, USA

Received 31 August 2014; Accepted 13 January 2015

Academic Editor: Walter Briec

Copyright © 2015 H. W. Corley and Phantipa Kwain. 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.


An algorithm is presented in this note for determining all Berge equilibria for an n-person game in normal form. This algorithm is based on the notion of disappointment, with the payoff matrix (PM) being transformed into a disappointment matrix (DM). The DM has the property that a pure strategy profile of the PM is a BE if and only if (0,…,0) is the corresponding entry of the DM. Furthermore, any (0,…,0) entry of the DM is also a more restrictive Berge-Vaisman equilibrium if and only if each player’s BE payoff is at least as large as the player’s maximin security level.