Proceedings of the 44th symposium on Theory of Computing - STOC '12, 2012
Using the powerful machinery of the linear complementarity problem and Lemke&... more Using the powerful machinery of the linear complementarity problem and Lemke's algorithm, we give a practical algorithm for computing an equilibrium for Arrow-Debreu markets under separable, piecewise-linear concave (SPLC) utilities, despite the PPAD-completeness of this case. As a corollary, we obtain the first elementary proof of existence of equilibrium for this case, i.e., without using fixed point theorems. In 1975,
We propose a new convex optimization formulation for the Fisher market problem with linear utilit... more We propose a new convex optimization formulation for the Fisher market problem with linear utilities. Like the Eisenberg-Gale formulation, the set of feasible points is a polyhedral convex set while the cost function is non-linear; however, unlike that, the optimum is always attained at a vertex of this polytope. The convex cost function depends only on the initial endowments of
Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em... more Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games with compact polytopal strategy sets and two payoff matrices (A,B) such that when (x,y) is the played strategy profile, the payoffs of the players are xAy and
Proceedings of the 44th symposium on Theory of Computing - STOC '12, 2012
Using the powerful machinery of the linear complementarity problem and Lemke&... more Using the powerful machinery of the linear complementarity problem and Lemke's algorithm, we give a practical algorithm for computing an equilibrium for Arrow-Debreu markets under separable, piecewise-linear concave (SPLC) utilities, despite the PPAD-completeness of this case. As a corollary, we obtain the first elementary proof of existence of equilibrium for this case, i.e., without using fixed point theorems. In 1975,
We propose a new convex optimization formulation for the Fisher market problem with linear utilit... more We propose a new convex optimization formulation for the Fisher market problem with linear utilities. Like the Eisenberg-Gale formulation, the set of feasible points is a polyhedral convex set while the cost function is non-linear; however, unlike that, the optimum is always attained at a vertex of this polytope. The convex cost function depends only on the initial endowments of
Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em... more Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games with compact polytopal strategy sets and two payoff matrices (A,B) such that when (x,y) is the played strategy profile, the payoffs of the players are xAy and
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Papers by Ruta Mehta