This tutorial will present a modular approach for identifying optimal and approximately optimal mechanisms for agents with multi-dimensional and non-linear preferences. The two running examples for the tutorial will be single-dimensional agents with a public budget, and multi-dimensional unit-demand agents. The modular approach identify families of optimal (or approximately optimal) single agent mechanisms and then construct from these families of mechanisms optimal (or approximately optimal) multi-agent mechanisms. Topics will include marginal revenue maximization, Border's inequality and extensions, Lagrangian virtual values, multi-dimensional virtual values, ex ante relaxations, the Bulow-Klemperer theorem and extensions, and correlation gap. See Chapters 5 and 6 of survey "Bayesian Mechanism Design" (Hartline, 2013).
The second session of this talk will take place on Thursday, August 27 from 10:00 am to 11:00 am.