Balancing supply and demand under bilateral constraints

Abstract

In a moneyless market, a nondisposable homogeneous commodity is reallocated between agents with single-peaked preferences. Agents are either suppliers or demanders. Transfers between a supplier and a demander are feasible only if they are linked. The links form an arbitrary bipartite graph. Typically, supply is short in one segment of the market, while demand is short in another. Our egalitarian transfer solution generalizes Sprumont's (1991) and Klaus et al.'s (1998) uniform allocation rules. It rations only the long side in each market segment, equalizing the net transfers of rationed agents as much as permitted by the bilateral constraints. It elicits a truthful report of both preferences and links: removing a feasible link is never profitable to either one of its two agents. Together with efficiency and a version of equal treatment of equals, these properties are characteristic. © 2012 Olivier Bochet, Rahmi İlki{dotless}li{dotless}ç, Hervé Moulin, and Jay Sethuraman

Allocation rules on networks

“…Our extension shows that most widely used principles of allocation are relevant also for this setting. Bochet et al (2012Bochet et al ( , 2013 and Szwagrzak (2011) have successfully adopted some axioms originally defined for simple allocation problems (e.g. equal treatment of equals, replacement principle etc.)…”

“…We provide an algorithm to extend a bilateral principle to an allocation rule which is pairwise robust. This algorithm is parallel to the ascending algorithms used in Moulin (1999) and Bochet et al (2013Bochet et al ( , 2012. Then, we show that each bilateral principle in this class has a unique extension which is pairwise robust with respect to the bilateral principle (Theorem 1).…”

“…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. A transfer is possible only between connected agents.…”

“…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).…”

Introduction to the special issue in honor of William Thomson

“…The next two papers are concerned with allocation among agents who have singlepeaked preferences (Sprumont 1991;Thomson 1995;Bochet et al 2012Bochet et al , 2013. In "Efficient, fair, and strategy-proof (re)allocation under network constraints," Karol Flores-Szwagrzak studies an allocation problem in which a resource is available in different "types" and has to be fully allocated among agents with single-peaked preferences, but there are constraints on the types that different agents can consume.…”