On Optimal Mechanisms in the Two-Item Single-Buyer Unit-Demand Setting

Understand

We consider the problem of designing a revenue-optimal mechanism in the two-item, single-buyer, unit-demand setting when the buyer's valuations, $(z_1, z_2)$, are uniformly distributed in an arbitrary rectangle $[c,c+b_1]\times[c,c+b_2]$ in the positive quadrant.

• We provide a complete and explicit solution for arbitrary nonnegative values of $(c,b_1,b_2)$.
• We identify five simple structures, each with at most five (possibly stochastic) menu items, and prove that the optimal mechanism has one of the five structures.
• We also characterize the optimal mechanism as a function of $b_1, b_2$, and $c$.