  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 (positive or
negative) as long as they satisfy superadditivity. For the case of additive
utilities, we present a characterization of allocations that can simultaneously
be made equitable and envy-free via payments.
