Achieving Envy-freeness and Equitability with Monetary Transfers

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