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Rank-1 Bi-matrix Games: A Homeomorphism and a Polynomial Time Algorithm
[article]
2010
arXiv
pre-print
Given a rank-1 bimatrix game (A,B), i.e., where rank(A+B)=1, we construct a suitable linear subspace of the rank-1 game space and show that this subspace is homeomorphic to its Nash equilibrium correspondence. Using this homeomorphism, we give the first polynomial time algorithm for computing an exact Nash equilibrium of a rank-1 bimatrix game. This settles an open question posed in Kannan and Theobald (SODA 2007) and Theobald (2007). In addition, we give a novel algorithm to enumerate all the
arXiv:1010.3083v2
fatcat:dnmsy2qeabhblogfnnybwl7z3a