私人帕累托最优交换
Private Pareto Optimal Exchange
摘要：
我们考虑的问题，实现个人理性的，渐进的帕累托最优分配在易货交换经济中，代理人被赋予货物和对他人的货物的偏好，但可能不使用货币作为交换媒介。由于这种经济的最重要的实例之一是肾脏交换-其中对问题的“输入“包括敏感的病人医疗记录-我们要问，在向参与者提供正式的隐私保证的同时，这种交换可以进行到什么程度。我们表明，单独合理的分配不能实现任何非平凡的近似帕累托最优，如果进行的约束下的差分隐私-甚至放松\emph{joint}差分隐私，根据它是已知的，渐近最优分配可以计算在双边市场，如果买家和卖家之间有区别，我们只关心买家的隐私~ \citep{Matching}。因此，我们考虑进一步放宽，我们称之为\emph{marginal}差分隐私-这承诺，非正式地说，每个代理$i$的隐私是保护从每个其他代理$j \neq i$，只要$j$不勾结或共享分配信息与其他代理。我们表明，在边际差分隐私，它是可能的，以计算一个单独的理性和渐近帕累托最优分配在这样的交换经济。
英文摘要：
We consider the problem of implementing an individually rational, asymptotically Pareto optimal allocation in a barter-exchange economy where agents are endowed with goods and have preferences over the goods of others, but may not use money as a medium of exchange. Because one of the most important instantiations of such economies is kidney exchange -- where the "input"to the problem consists of sensitive patient medical records -- we ask to what extent such exchanges can be carried out while providing formal privacy guarantees to the participants. We show that individually rational allocations cannot achieve any non-trivial approximation to Pareto optimality if carried out under the constraint of differential privacy -- or even the relaxation of \emph{joint} differential privacy, under which it is known that asymptotically optimal allocations can be computed in two-sided markets, where there is a distinction between buyers and sellers and we are concerned only with privacy of the buyers~\citep{Matching}. We therefore consider a further relaxation that we call \emph{marginal} differential privacy -- which promises, informally, that the privacy of every agent $i$ is protected from every other agent $j \neq i$ so long as $j$ does not collude or share allocation information with other agents. We show that, under marginal differential privacy, it is possible to compute an individually rational and asymptotically Pareto optimal allocation in such exchange economies.
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