Achieving Envy-freeness and Equitability with Monetary Transfers

Abstract

When allocating indivisible resources or tasks, an envy-free allocation or equitable allocation may not exist. We present a sufficient condition and an algorithm to achieve envy-freeness and equitability when monetary transfers are allowed. The approach works for any agent valuation functions as long as they satisfy superadditivity. For the case of additive valuations, we present a characterization of allocations that can simultaneously be made equitable and envy-free via payments. We then present a distributed algorithm to compute an approximately envy-free outcome for any class of valuations.