Fair and Truthful Mechanism with Limited Subsidy

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, subsidize envious agents. In paper, we aim design truthful allocation mechanism goods achieve both efficiency criteria with limited amount subsidy. Following the work Halpern Shah, our central question as follows: what extent do need rely on power money accomplish these objectives? For general valuations, impossibility theorem combinatorial auction translates setting: even if arbitrarily large available for use, no can truthfulness, envy-freeness, utilitarian optimality simultaneously when agents monotone submodular valuations. By contrast, show that, matroidal there that achieves envy-freeness subsidizing each agent at most $1$, maximum marginal contribution item agent. rests crucially underlying M-convexity Lorenz dominating allocations.