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Exploiting the algebraic structure of the set of bimatrix games, a divide-and-conquer algorithm for finding Nash equilibria is proposed. The algorithm is fixed-parameter tractable with the size of the largest irreducible component of a game as parameter. An implementation of the algorithm is shown to yield a significant performance increase on inputs with small parameters.doi:10.4204/eptcs.146.10 fatcat:iy6bjjsmmjgj7hdtqjgahd65pm