A two-dimensional problem of revenue maximization

► Examining an optimal mechanism for a seller of two exclusive products and one buyer. ► For many buyer-product value distributions, we characterize the mechanism near the axes. ► Close to the axes, as was to be expected, our characterization collapses to the single dimension case. ► Uniform distribution on the triangular domain: the mechanism is piecewise linear, 3 parts at most. ► We obtain explicit mechanism formulas for many cases of interest.