A Double-Sided Multiunit Combinatorial Auction for Substitutes: Theory and Algorithms

Combinatorial exchanges have existed for a long time in securities markets. In these auctions buyers and sellers can place orders on combinations, or bundles of different securities. These orders are conjunctive: they are matched only if the full bundle is available. On business-to-business (B2B) exchanges, buyers have the choice to receive the same product with different attributes; for instance the same product can be produced by different sellers. A buyer indicates his preference by submitting a disjunctive order, where he specifies how much of the product he wants, and how much he values each attribute. Only the goods with the best attributes and prices will be matched. This article considers a doubled-sided multi-unit combinatorial auction for substitutes, that is, a uniform price auction where buyers and sellers place both types of orders, conjunctive and disjunctive. We prove the existence of a linear price which is both competitive and surplus-maximizing when goods are perfectly divisible, and nearly so otherwise. We describe an algorithm to clear the market, which is particularly efficient when the number of traders is large.Combinatorial auction, economic equilibrium

Anonymous Price Taking Equilibrium in Tiebout Economies with Unbounded Club Sizes

We introduce a model of a local public goods economy with a continuum of agents and jurisdictions with finite, but unbounded populations. Under boundedness of per capita payoffs we demonstrate nonemptiness of the core of the economy. We then demonstrate that the equal treatment core coincides with the set of price-taking equilibrium outcomes with anonymous prices - that is, prices for public goods depend only on observable characteristics of agents. Existence of equilibrium follows from nonemptiness of the core and equivalence of the core to the set of equilibrium outcomes. Our approach provides a new technique for showing existence of equilibrium in economies with a continuum of agents.Tiebout, Clubs, Jurisdictions, F-core, Core-equilibrium equivalence, Edgeworth equivalence, Continuum economies with clubs, Crowding types, Core, Equal treatment core

Competitive Equilibria in Economies with Multiple Divisible and Multiple Divisible Commodities

In this paper we consider a general equilibrium model with a finite number of divisible and indivisible commodities.In models with indivisibilities it is typically assumed that there is only one perfectly divisible good, which serves as money.The presence of money in the model is used to transfer the value of certain amounts of indivisible goods.For such economies with one divisible commodity Danilov et al. showed the existence of a general equilibrium if the individual demands and supplies belong to a same class of discrete convexity.For economies with multiple divisible goods and money van der Laan et al. proved existence of a general equilibrium if the divisible goods are produced out of money using a linear production technology and no other producers are present in the model.In the models to be presented in this paper we allow for multiple divisible commodities and a finite number of producers with non-increasing returns to scale technologies.Convexity is replaced by pseudoconvexity, while the indivisible parts of individual demands and supply should belong to some class of discrete convexity.In the first model money is present.Money is strictly desired by the consumers like in the other models, is indispensable for production and enough money should be present in the economy.To guarantee existence of a general equilibrium individual demands and supplies should be products of divisible and indivisible parts.In the second model there is no money, but at least one linear production technology is present in order to produce the divisible goods.Individual endowments being sufficienly large for production guarantee the existence of a competitive equilibrium.

The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects

We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents' substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability---which is a strictly weaker condition than gross substitutability---is sufficient for the existence of competitive equilibrium. We also extend the ``demand types'' classification of valuations to settings with income effects and give necessary and sufficient conditions for a pattern of substitution effects to guarantee the existence of competitive equilibrium.Comment: 46 pages, 1 figur

Herbert Scarf: a Distinguished American Economist

Herbert Eli Scarf (born on July 25, 1930 in Philadelphia, PA) is a distinguished American economist and Sterling Professor (Emeritus as of 2010) of Economics at Yale University. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences and the American Philosophical Society. He served as the president of the Econometric Society in 1983. He received both the Frederick Lanchester Award in 1973 and the John von Neumann Medal in 1983 from the Operations Research Society of America and was elected as a Distinguished Fellow of the American Economic Association in 1991.