Envy-free allocation of indivisible goods with money and externalities

This paper considers an envy-free allocation of a single indivisible good in the quasi-linear utility environment where a monetary transfer is allowed and externalities among agents exist. We show that an envy-free allocation does not exist if a degree of the externalities is high enough and there are two groups of agents: one group of agents can but the other group of agents cannot enjoy externalities. We also show that both efficient allocations and envy-free allocations are generally incompatible whereas they are always compatible without externalities.