Abstract
Utility functions satisfying gross substitutability have been studied extensively in the economics literature [1,11,12] and recently, the importance of this property has been recognized in the design of combinatorial polynomial time market equilibrium algorithms [8]. This naturally raises the following question: is it possible to design a combinatorial polynomial time algorithm for this general class of utility functions? We partially answer this question by giving an algorithm for separable, differentiable, concave utility functions satisfying gross substitutes. Our algorithm uses the auction based approach of [10].
We also outline an extension of our method to the Walrasian model.
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Garg, R., Kapoor, S., Vazirani, V. (2004). An Auction-Based Market Equilibrium Algorithm for the Separable Gross Substitutability Case. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2004 2004. Lecture Notes in Computer Science, vol 3122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27821-4_12
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DOI: https://doi.org/10.1007/978-3-540-27821-4_12
Publisher Name: Springer, Berlin, Heidelberg
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