# Multi-Dimensional and Non-Linear Mechanism Design and Approximation

#### This series of talks was part of the Economics and Computation Boot Camp. Videos for each talk area available through the links above.

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).