TY - GEN
T1 - Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items
AU - Murota, Kazuo
AU - Shioura, Akiyoshi
AU - Yang, Zaifu
PY - 2013
Y1 - 2013
N2 - We address the problem of computing a Walrasian equilibrium price in an ascending auction with gross substitutes valuations. In particular, an auction market is considered where there are multiple differentiated items and each item may have multiple units. Although the ascending auction is known to find an equilibrium price vector in finite time, little is known about its time complexity. The main aim of this paper is to analyze the time complexity of the ascending auction globally and locally, by utilizing the theory of discrete convex analysis. An exact bound on the number of iterations is given in terms of the ℓ∞ distance between the initial price vector and an equilibrium, and an efficient algorithm to update a price vector is designedbased on a min-max theorem for submodular function minimization.
AB - We address the problem of computing a Walrasian equilibrium price in an ascending auction with gross substitutes valuations. In particular, an auction market is considered where there are multiple differentiated items and each item may have multiple units. Although the ascending auction is known to find an equilibrium price vector in finite time, little is known about its time complexity. The main aim of this paper is to analyze the time complexity of the ascending auction globally and locally, by utilizing the theory of discrete convex analysis. An exact bound on the number of iterations is given in terms of the ℓ∞ distance between the initial price vector and an equilibrium, and an efficient algorithm to update a price vector is designedbased on a min-max theorem for submodular function minimization.
UR - http://www.scopus.com/inward/record.url?scp=84893396469&partnerID=8YFLogxK
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U2 - 10.1007/978-3-642-45030-3_44
DO - 10.1007/978-3-642-45030-3_44
M3 - Conference contribution
AN - SCOPUS:84893396469
SN - 9783642450297
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 468
EP - 478
BT - Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings
T2 - 24th International Symposium on Algorithms and Computation, ISAAC 2013
Y2 - 16 December 2013 through 18 December 2013
ER -