Substitute Valuations, Auctions, and Equilibrium with Discrete Goods

Paul Milgrom () and Bruno Stulovici

No 339, Economics Series Working Papers from University of Oxford, Department of Economics

Abstract: For economies in which goods are available in several (discrete) units, this paper identifies two notions of substitutes. The weaker notion guarantees monotonicity of tatonnement processses and convergence of clock auctions to a pseudo-equilibrium, but only the stronger notion, which treats each unit traded as a distinct good with its own price, guarantees that every pseudo-equilibrium is a Walrasian equilibrium, the Vickrey outcome is in the core, and the "law of aggregate demand" is satisfied. The paper provides several characterizations and properties of weak and strong substitutes.

Keywords: Substitute Valuation; Auction; Discrete Goods; Nonlinear Price; Submodular Dual; Walrasian Equilibrium; Pseudo-Equilibrium; Law of Aggregate Demand; Vickrey Auction (search for similar items in EconPapers)
JEL-codes: D44 C62 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2007
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Working Paper: Substitute Valuations, Auctions and Equilibrium with Discrete Goods (2006)
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