On Representatives of Subsets

Hall, Philip

doi:10.1112/jlms/s1-10.37.26

Cited by 1,547 publications

(480 citation statements)

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“…This finding generalizes a result of Kranton and Minehart (2000). 20 While Kranton and Minehart restrict attention to assignment games derived from networks with homogeneous goods, Gul and Stacchetti (2000) obtain a general version of this result for settings with multi-unit demand for heterogeneous goods and utility functions that satisfy the gross substitutes condition.…”

Section: Theorem 9 (Kranton and Minehartmentioning

confidence: 50%

“…The first part of the result of Kranton and Minehart refines this conclusion by addressing the issue of interim incentives in the dynamic environment of the simultaneous auction mechanism. 20 The intuition for the result on efficient network formation is that the positive welfare externalities 18 Prices increase continuously and each buyer decides at every point whether to continue competing in or drop out of the auction of any linked seller. Maximal submarkets induced by the network of buyer-seller pairs (i, j) with the property that buyer i has not dropped out of seller j's auction are cleared as prices increase.…”

Section: Theorem 9 (Kranton and Minehartmentioning

confidence: 99%

“…If ij ∈ H then we say that i and j are matched (with each other) under H. A matching of G is perfect if it covers all the nodes in G. Matchings of G that contain the largest number of links are called maximum matchings. The cardinality of the maximum matchings of G defines the maximum total surplus in G. For example, in A simple condition due to Hall (1935) characterizes the bipartite networks which admit perfect matchings. More generally, Hall's theorem provides a necessary and sufficient condition for such networks to contain matchings that cover all the buyers (or sellers).…”

Section: Frameworkmentioning

confidence: 99%

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Models of Bilateral Trade in Networks

Manea

2016

The Oxford Handbook of the Economics of Networks

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Section: Theorem 9 (Kranton and Minehartmentioning

confidence: 50%

Section: Theorem 9 (Kranton and Minehartmentioning

confidence: 99%

Section: Frameworkmentioning

confidence: 99%

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Models of Bilateral Trade in Networks

Manea

2016

The Oxford Handbook of the Economics of Networks

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“…That is, a competitive matching for the price vector p exists if and only if there is no underdemanded set at prices p (Hall, 1935), Gale and Shapley (1962), Dantzig (1963)). …”

Section: The Competitive Market and The Auction Mechanismmentioning

confidence: 99%

A simultaneous descending bid auction for multiple items and unitary demand

Sotomayor¹

2002

Rev. Bras. Econ.

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Summary: 1. Introduction; 2. The competitive market and the auction mechanism; 3. The main results; 4. Concluding remarks.Keywords: auction mechanism; competitive equilibrium; demand set.JEL codes: C78 and D78. This paper proposes a new descending bid method for auctioning multiple objects. The auctioneer announces a current price, bidders indicate their demands at that price, and the auctioneer lowers the prices until every object can be allocated to a buyer who demands it and no buyer receives more than one item. The features of this mechanism lie on the facts that: the objects are sold simultaneously at prices that clear the market; every two similar objects are sold at the same price; the mechanism always produces the same final price, namely, the maximum competitive equilibrium price. In addition, the auctioneer can choose an efficient allocation.Este artigo propõe um novo método de lances descendentes para leiloar múltiplos objetos com demanda unitária. O leiloeiro anuncia um preço, os compradores indicam suas demandas ao preço anunciado, e o leiloeiro desce os preços até que todo objeto esteja alocado para algum comprador que o tenha demandado e ninguém esteja comprando mais do que um item. Os aspectos importantes deste mecanismo são que os objetos são vendidos simultaneamente a preços competitivos, quaisquer dois objetos similares são vendidos ao mesmo preço e independentemente das escolhas do leiloeiro o mecanismo sempre produz o mesmo preço final, o preço máximo de equilíbrio competitivo. Além disso,é sempre possível para o leiloeiro escolher uma alocação eficiente.

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“…Theorem 6.11. Hall's marriage theorem [12]. Let S = {S 1 , ..., S n } be a collection of finite subsets of some larger set.…”

Section: Essential Critical Pointsmentioning

confidence: 99%