A new polynomial-time algorithm for linear programming
Combinatorica
Stability and perfection of Nash equilibria
Stability and perfection of Nash equilibria
The nucleolus of a matrix game and other nucleoli
Mathematics of Operations Research
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Computing sequential equilibria for two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fast algorithms for finding proper strategies in game trees
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Computing proper equilibria of zero-sum games
CG'06 Proceedings of the 5th international conference on Computers and games
On proper refinement of Nash equilibria for bimatrix games
Automatica (Journal of IFAC)
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We provide the first pivoting-type algorithm that computes an exact proper equilibrium of a bimatrix game. This is achieved by using Lemke's algorithm to solve a linear complementarity problem (LCP) of polynomial size. This also proves that computing a simple refinement of proper equilibria for bimatrix game is PPAD-complete. The algorithm also computes a witness in the form of a parameterized strategy that is an epsilon-proper equilibrium for any given sufficiently small epsilon, allowing polynomial-time verification of the properties of the refined equilibrium. The same technique can be applied to matrix games (two-player zero-sum), thereby computing a parameterized epsilon-proper strategy in polynomial time using linear programming.