Clearing supply and demand under bilateral constraints

Abstract

In a moneyless market, a non storable, non transferable 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, and the links form an arbitrary bipartite graph. Typically, supply is short in one segment of the market, while demand is short in another.Information about individual preferences is private, and so is information about feasible links: an agent may unilaterally close one of her links if it is in her interest to do so.Our egalitarian transfer solution 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 pro table to either one of its two agents. Together with e ciency, and a version of equal treatment of equals, these properties are characteristic.

The Bipartite Rationing Problem

“…It is easy to check that for any fixed λ and µ, the minimum is attained in (9) uniquely by the solution ϕ * ia = e λi+µ a , using which we get…”

“…Bochet et al [9] is a variant of [8] with strategic agents on both sources and sinks, the source-agents demanding some resource up to some privately held peak level, while the sink agents want to supply resource up to their own peak level. Efficient trade splits the market in a segment where suppliers get their peak allocation while the relevant demanders are rationed, and another segment where the roles are reversed.…”

“…Random assignment under dichotomous preferences, studied by Bogomolnaia and Moulin [7] and Roth et al [37], is the special case of [9] where all claims are for one unit and there is one unit of each resource-type. In that model as here, the assumption of unit claims and unit types does not significantly simplify the computations.…”

“…It is well known (see [1] or [9]) that the system of inequalities (3), shown below, characterizes the existence of a flow ϕ exhausting all resources and transferring at most his claim to each agent i.…”

Rationing problems in bipartite networks

“…It is a happy coincidence that this method is also consistent. In a recent series of papers, Bochet et al [2011;2012] study these questions in the bipartite framework and propose the egalitarian mechanism that generalizes the uniform gains method to the bipartite setting. Unfortunately the method underlying their mechanism fails consistency.…”