On Stable Matchings and Flows

Fleiner, Tamás

doi:10.3390/a7010001

Cited by 28 publications

(44 citation statements)

References 10 publications

(9 reference statements)

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“…those immune to coordinated deviations by a set of firms which is simultaneously signing a trail of contracts. Our paper is also related to the stability of (continuous and discrete) network flows discussed by Fleiner (2009Fleiner ( , 2014. In these models, agents choose the amount of "flow" they receive from upstream and downstream agents and have preferences over who they receive the "flow" from.…”

Section: Introductionmentioning

confidence: 99%

Trading networks with bilateral contracts

Fleiner

Jankó

Tamura

et al. 2015

Proceedings of the the Third Conference on Auctions, Market Mechanisms and Their Applications

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We consider general networks of bilateral contracts that include supply chains. We define a new stability concept, called trail stability, and show that any network of bilateral contracts has a trailstable outcome whenever agents' choice functions satisfy full substitutability. Trail stability is a natural extension of chain stability, but is a stronger solution concept in general contract networks. Trail-stable outcomes are not immune to deviations of arbitrary sets of firms. In fact, we show that outcomes satisfying an even more demanding stability property -full trail stability -always exist. For fully trailstable outcomes, we prove results on the lattice structure, the rural hospitals theorem, strategy-proofness and comparative statics of firm entry and exit. We pin down a condition under which trail-stable and fully trail-stable outcomes coincide. We then completely describe the relationships between various other concepts. When contracts specify trades and prices, we also show that competitive equilibrium exists in networked markets even in the absence of fully transferrable utility. The competitive equilibrium outcome is (fully) trail-stable.Keywords: trail stability, chain stability, set stability, matching markets, supply chains, networks, contracts, competitive equilibrium.JEL Classification: C78, L14 * We would like to thank Samson Alva, Scott Kominers and Michael Ostrovsky for their valuable comments on the recent versions of the paper. Vincent Crawford, Umut Dur, Jens Gudmundsson, Claudia Herrestahl, Paul Klemperer, Collin Raymond, and Zaifu Yang also gave great comments on much earlier drafts. We had enlightening conversations with Alex Nichifor, Alex Westkamp and M. Bumin Yenmez about the project. Moreover, we are also grateful to seminar participants at the Southern

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Section: Introductionmentioning

confidence: 99%

Trading networks with bilateral contracts

Fleiner

Jankó

Tamura

et al. 2015

Proceedings of the the Third Conference on Auctions, Market Mechanisms and Their Applications

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“…Ostrovsky [21] newly defined the concepts of same-side substitutability and cross-side complementarity, and proved that if choice functions of the agents satisfy these two conditions then there always exists a chain stable allocation, (see the next section for details.) Fleiner [6] also imported the concept of stability into the discrete/continuous flow problem, and generalized the lattice structure of stable marriages.…”

Section: Introductionmentioning

confidence: 99%

Stability in Supply Chain Networks: An Approach by Discrete Convex Analysis

Ikebe

Tamura

2015

JORSJ

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Ostrovsky generalized the stable marriage model of Gale and Shapley to a model on an acyclic directed graph, and showed the existence of a chain stable allocation under the conditions called sameside substitutability and cross-side complementarity. In this paper, we extend Ostrovsky's model and the concepts of same-side substitutability and cross-side complementarity by using value functions which are defined on integral vectors and allow indifference. We give a characterization of chain stability under the extended versions of same-side substitutability and cross-side complementarity, and develop an algorithm which always finds a chain stable allocation. We also verify that twisted M ♮ -concave functions, which are variants of M ♮ -concave functions central to discrete convex analysis, satisfy these extended conditions. For twisted M ♮ -concave value functions of the agents, we analyze the time-complexity of our algorithm.

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“…Fleiner [2] proved the following result, by reducing the stable flow problem to the stable allocation problem of Baïou and Balinski [3]. A different proof based on the Gale-Shapley algorithm, as well as an extension to flows over time, was given by Cseh, Matuschke, and Skutella [4].…”

Section: Introductionmentioning

confidence: 99%

“…An acyclic network model was presented by Ostrovsky [1], while Fleiner [2] introduced a stable flow model where the network is not necessarily acyclic. The aim of this paper is to extend the model of Fleiner to multicommodity flows, but first we briefly describe his model and results.…”

Section: Introductionmentioning

confidence: 99%

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Stable Multicommodity Flows

Király

Pap

2013

Algorithms

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We extend the stable flow model of Fleiner to multicommodity flows. In addition to the preference lists of agents on trading partners for each commodity, every trading pair has a preference list on the commodities that the seller can sell to the buyer. A blocking walk (with respect to a certain commodity) may include saturated arcs, provided that a positive amount of less preferred commodity is traded along the arc. We prove that a stable multicommodity flow always exists, although it is PPAD-hard to find one.

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On Stable Matchings and Flows

Cited by 28 publications

References 10 publications

Trading networks with bilateral contracts

Trading networks with bilateral contracts

Stability in Supply Chain Networks: An Approach by Discrete Convex Analysis

Stable Multicommodity Flows

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