The notion of \emph{envy-freeness} is a natural and intuitive fairness requirement in resource allocation. With indivisible goods, such fair allocations are unfortunately not guaranteed to exist. Classical works have avoided this issue by introducing an additional divisible resource, i.e., money, to subsidize envious agents. In this paper, we aim to design a truthful allocation mechanism of indivisible goods to achieve both fairness and efficiency criteria with a limited amount of subsidy. Following the work of Halpern and Shah, our central question is as follows: to what extent do we need to rely on the power of money to accomplish these objectives? For general valuations, the impossibility theorem of combinatorial auction translates to our setting: even if an arbitrarily large amount of money is available for use, no mechanism can achieve truthfulness, envy-freeness, and utilitarian optimality simultaneously when agents have general monotone submodular valuations. By contrast, we show that, when agents have matroidal valuations, there is a truthful allocation mechanism that achieves envy-freeness and utilitarian optimality by subsidizing each agent with at most $1$, the maximum marginal contribution of each item for each agent. The design of the mechanism rests crucially on the underlying matroidal M-convexity of the Lorenz dominating allocations.

翻译：\ emph{ envy- freeness} 的概念是资源分配中自然和直觉的公平性要求。 由于不可分割的商品,这种公平分配是无法保证的。 古典作品避免了这个问题,引入了额外的可分的资源,即金钱,补贴不知情的代理人。 在本文中,我们的目标是设计一个不可分割商品的真正分配机制,以达到公平和效率标准,并有有限的补贴。 在Halpern和Shah的工作之后,我们的核心问题是:我们在多大程度上需要依靠资金的力量来实现这些目标?对于一般估价来说,不可能有组合拍卖的标本可以转化为我们的环境:即使任意地有大量资金可供使用,但没有任何机制能够同时实现真实性、无嫉妒性和实用性的最佳性,当代理人拥有一般的单调亚货币亚货币的亚货币价值时。相反,我们表明,当代理人有对黄金估值时,我们有一个真实的分配机制,通过对每个边缘的代理人进行嫉妒性和实用性最佳最佳最佳分配方式,通过对每个核心的代理人进行最高一美元设计机制进行补贴。