Optimal Allocation of an Indivisible Good

In this paper, we consider the problem of allocating an indivisible good between two agents under incomplete information. We provide a characterization of mechanisms that maximize the sum of the expected utilities of the agents among all deterministic feasible strategy-proof mechanisms: Any optimal mechanism must belong to either one of the two fixed-price mechanisms or one of the two option mechanisms. Furthermore, when stochastic mechanisms are allowed and agents' types are distributed uniformly, we show that any optimal mechanism must be a convex combination of two fixed-price mechanisms and two option mechanisms