Abstract
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 the buyers. This formulation yields an easy simplex-like pivoting algorithm which is provably strongly polynomial for many special cases.
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Adsul, B., Babu, C.S., Garg, J., Mehta, R., Sohoni, M. (2010). A Simplex-Like Algorithm for Fisher Markets. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds) Algorithmic Game Theory. SAGT 2010. Lecture Notes in Computer Science, vol 6386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16170-4_3
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DOI: https://doi.org/10.1007/978-3-642-16170-4_3
Publisher Name: Springer, Berlin, Heidelberg
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