Example: Optimal Auctions for Beta Distributions

This example considers the case of 2 items and a single additive buyer whose values are distributed independently according to Beta distributions. Note that in the special case with Beta(1,1), the value for each item is distributed uniformly in [0,1].

  1. a1 =   b1 =
  2. a2 =   b2 =

The figure shows how the framework in the papers "Mechanism Design via Optimal Transport" and "Strong Duality for a Multiple-Good Monopolist" can be applied to compute the optimal mechanism that maximizes the seller's expected revenue: