[Sequence announcement] Introduction to Mechanism Design

Mechanism design is the theory of how to construct institutions for strategic agents, spanning applications like voting systems, school admissions, regulation of monopolists, and auction design. Think of it as the engineering side of game theory, building algorithms for strategic agents. While it doesn’t have much to say about rationality directly, mechanism design provides tools and results for anyone interested in world optimization.

In this sequence, I’ll touch on

  • The basic mechanism design framework, including the revelation principle and incentive compatibility.

  • The Gibbard-Satterthwaite impossibility theorem for strategyproof implementation (a close analogue of Arrow’s Theorem), and restricted domains like single-peaked or quasilinear preference where we do have positive results.

  • The power and limitations of Vickrey-Clarke-Groves mechanisms for efficiently allocating goods, generalizing Vickrey’s second-price auction.

  • Characterizations of incentive-compatible mechanisms and the revenue equivalence theorem.

  • Profit-maximizing auctions.

  • The Myerson-Satterthwaite impossibility for bilateral trade.

  • Two-sided matching markets à la Gale and Shapley, school choice, and kidney exchange.

As the list above suggests, this sequence is going to be semi-technical, but my foremost goal is to convey the intuition behind these results. Since mechanism design builds on game theory, take a look at Yvain’s Game Theory Intro if you want to brush up.

Various resources:

I plan on following up on this sequence with another focusing on group rationality and information aggregation, surveying scoring rules and prediction markets among other topics.

Suggestions and comments are very welcome.