The Bipartite Rationing Problem

Moulin, Hervé; Sethuraman, Jay

doi:10.1287/opre.2013.1199

Cited by 26 publications

(33 citation statements)

References 35 publications

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“…Bjørndal and Jörnsten (2009) analyze generalized bankruptcy problems with multiples estates as flow sharing problems and define the nucleolus and the constrained egalitarian solution for such problems. Moulin and Sethuraman (2013) consider bipartite rationing problems, where agents can have claims on a subset of unrelated estates. They consider whether rules for single resource problems can be consistently extended to their framework.…”

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confidence: 99%

Decentralized Clearing in Financial Networks

Csóka

Herings

2018

Management Science

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We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. We present a convenient representation of bankruptcy rules. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure. Abstract We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. We present a convenient representation of bankruptcy rules.A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure.

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confidence: 99%

Decentralized Clearing in Financial Networks

Csóka

Herings

2018

Management Science

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“…Our example also shows that pairwise robustness is different from the joint requirement of node-consistency and edge-consistency. Even though both our paper and Moulin and Sethuraman (2013) give a unique extension of the proportional principle, those extensions are not equivalent. Bochet et al (2012) study a similar model where suppliers and demanders of a homogeneous commodity are embedded in a bipartite network.…”

Section: Introductionmentioning

confidence: 88%

“…Several allocation rules for allocation problems on networks have recently been introduced and axiomatized in Branzei et al (2008), Bjørndal and Jörnsten (2010), Bochet et al (2012Bochet et al ( , 2013, Moulin andSethuraman (2013), andSzwagrzak (2011). One way to study allocation rules on networks is to represent the allocation problem as a network flow problem where transfers between nodes are costly and analyze the related minimum cost flow problem on a simple network and implement some known principles for simple allocation problems via suitable cost functions (Branzei et al 2008).…”

Section: Introductionmentioning

confidence: 99%

“…An alternative extension of simple allocation rules is in a node-consistent fashion, i.e., in addition to agent-consistency, if a source leaves the problem with its endowment and the corresponding amounts are reduced from the claims of the agents' who were receiving them from the source, then the new problem should assign the agents the amounts they received in the original problem minus the amounts allocated from the deleted source (Moulin and Sethuraman 2013). Another requirement in Moulin and Sethuraman (2013) is edge-consistency which requires that if an edge is deleted from the network of the original problem and the agent's claim and the endowment of the source which formed the deleted link is decreased by the amount flowing to the agent from this source, then at the new problem the agent's allocation should be equal to the original allocation minus the amount which the deleted link used to carry.…”

Section: Introductionmentioning

confidence: 99%

“…Another requirement in Moulin and Sethuraman (2013) is edge-consistency which requires that if an edge is deleted from the network of the original problem and the agent's claim and the endowment of the source which formed the deleted link is decreased by the amount flowing to the agent from this source, then at the new problem the agent's allocation should be equal to the original allocation minus the amount which the deleted link used to carry. This is a more demanding condition than node-consistency and it means that the agents are held responsible for their connections.…”

Section: Introductionmentioning

confidence: 99%

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Allocation rules on networks

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2014

Soc Choice Welf

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When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and a citizen depicts the possibility of a transfer from the source to the citizen. Given the endowments at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on resource monotonic and anonymous bilateral principles satisfying a regularity condition and extend these principles to allocation rules on networks. We require the extension to preserve the essence of the bilateral principle for each pair of citizens in the network. We call this condition pairwise robustness with respect to the bilateral principle. We provide an algorithm and show that each bilateral principle has a unique extension which is pairwise robust (Theorem 1). Next, we consider a Rawlsian criteria of distributive justice and show that there is a unique "Rawls fair" rule that equals the extension given by the algorithm (Theorem 2). Pairwise robustness and Rawlsian fairness are two sides of the same coin, the former being a pairwise and the latter a global requirement on the allocation given by a rule. We also show as a corollary that any parametric principle can be extended to an allocation rule (Corollary 1). Finally, we give applications of the algorithm for the egalitarian, the proportional, and the contested garment bilateral principles (Example 1).

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On solving mutual liability problems

2017

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This paper introduces mutual liability problems, as a generalization of bankruptcy problems, where every agent not only owns a certain amount of cash money, but also has outstanding claims and debts towards the other agents. Assuming that the agents want to cash their claims, we will analyze mutual liability rules which prescribe how the total available amount of cash should be allocated among the agents. We in particular focus on bilateral -transfer schemes, which are based on a bankruptcy rule . Although in general a -transfer scheme need not be unique, we show that the resulting -transfer allocation is. This leads to the definition of -based mutual liability rules. For so called hierarchical mutual liability problems an alternative characterization of -based mutual liability rules is provided. Moreover it is shown that the axiomatic characterization of the Talmud rule on the basis of consistency can be extended to the corresponding mutual liability rule.

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The Bipartite Rationing Problem

Cited by 26 publications

References 35 publications

Decentralized Clearing in Financial Networks

Decentralized Clearing in Financial Networks

Allocation rules on networks

On solving mutual liability problems

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