Computing a Walrasian Equilibrium in Iterative Auctions with Multiple Differentiated Items
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.
KeywordsLyapunov Function Price Vector Valuation Function Combinatorial Auction Submodular Function
Unable to display preview. Download preview PDF.
- 2.Ausubel, L.M., Milgrom, P.: Ascending auctions with package bidding. Front. Theor. Econ. 1, Article 1 (2002)Google Scholar
- 4.Bing, M., Lehmann, D., Milgrom, P.: Presentation and structure of substitutes valuations. In: Proc. EC 2004, pp. 238–239 (2004)Google Scholar
- 5.Blumrosen, L., Nisan, N.: Combinatorial auction. In: Nisan, N., et al. (eds.) Algorithmic Game Theory, pp. 267–299. Cambridge Univ. Press (2007)Google Scholar
- 6.Cramton, P., Shoham, Y., Steinberg, R.: Combinatorial Auctions. MIT Press (2006)Google Scholar
- 7.Fujishige, S.: Submodular Functions and Optimization, 2nd edn. Elsevier (2005)Google Scholar
- 20.Parkes, D.C., Ungar, L.H.: Iterative combinatorial auctions: theory and practice. In: Proc. 17th National Conference on Artificial Intelligence (AAAI 2000), pp. 74–81 (2000)Google Scholar