This book has three parts, each with its own overarching goal. Lectures 2–10 develop tools for designing systems with strategic participants that have good performance guarantees. The goal of Lectures 11–15 is to understand when selfish behavior is largely benign. Lectures 16–20 study if and how strategic players reach an equilibrium of a game. The three sections of this lecture offer motivating examples for the three parts of the book.

The Science of Rule-Making

We begin with a cautionary tale. In 2012, the Olympics were held in London. One of the biggest scandals of the event concerned, of all sports, women's badminton. The scandal did not involve any failed drug tests, but rather a failed tournament design that did not carefully consider incentives.

The tournament design used is familiar from World Cup soccer. There are four groups (A, B, C, D) of four teams each. The tournament has two phases. In the first “round-robin” phase, each team plays the other three teams in its group, and does not play teams in other groups. The top two teams from each group advance to the second phase, while the bottom two teams from each group are eliminated. In the second phase, the remaining eight teams play a standard “knockout” tournament. There are four quarterfinals, with the losers eliminated, followed by two semifinals, with the losers playing an extra match to decide the bronze medal. The winner of the final gets the gold medal, the loser the silver.

The incentives of participants and of the Olympic Committee and fans are not necessarily aligned in such a tournament. What does a team want? To get as prestigious a medal as possible. What does the Olympic Committee want? They didn't seem to think carefully about this question, but in hindsight it is clear that they wanted every team to try their best to win every match. Why would a team ever want to lose a match? Indeed, in the knockout phase of the tournament, where losing leads to instant elimination, it is clear that winning is always better than losing.

Last lecture proved generic tight bounds on the price of anarchy (POA) of selfish routing, parameterized by the edge cost functions. One particular instantiation of these bounds gives a rigorous justification for the common strategy of over-provisioning a communication network to achieve good performance (Section 12.1). A different result in the same vein states that a modest technology upgrade improves network performance more than implementing dictatorial control (Sections 12.2-12.3). Applications in which network users control a non-negligible fraction of the traffic are best modeled via an “atomic” variant of selfish routing (Section 12.4). The POA of atomic selfish routing is larger than in the “nonatomic” model, but remains bounded provided the network cost functions are affine (Sections 12.4-12.5), or more generally “not too nonlinear.”

Case Study: Network Over-Provisioning

Motivation

The study of selfish routing provides insight into many different kinds of networks, including transportation, communication, and electrical networks. One big advantage in communication networks is that it is often relatively cheap to add additional capacity to a network. Because of this, a popular strategy to communication network management is to install more capacity than is needed, meaning that the network will generally not be close to fully utilized. One motivation for such network over-provisioning is to anticipate future growth in demand. Over-provisioning is also used for performance reasons, as it has been observed empirically that networks tend to suffer fewer packet drops and delays when they have extra capacity.

Lecture 2 introduced the quasilinear utility model, where each agent acts to maximize her valuation of the chosen outcome, less the pay-ment she makes. We placed no restrictions on payments other than the modest conditions that they are nonnegative and guarantee non-negative utility to truthful bidders. This lecture is the first to consider mechanism design problems with payment constraints, in addition to the usual incentive and feasibility constraints.

Section 9.1 extends the quasilinear utility model to accommodate budget constraints. Section 9.2 studies multi-unit auctions where bidders have budgets, and proposes an elegant if non-DSIC solution: the uniform-price auction. The clinching auction, described in Sec-tion 9.3, is a more complex auction for the same problem that is DSIC. Section 9.4 considers mechanism design with no payments whatsoever, introduces the canonical house allocation problem, and studies the properties of the Top Trading Cycle algorithm.

Budget Constraints

In many applications, there are constraints on the payments charged by a mechanism. Exhibit A is budget constraints, which limit the amount of money that an agent can pay. Budgets are especially relevant in auctions where an agent might buy a large number of items. For example, in the sponsored search auctions (Section 2.6) used in practice, every bidder is asked for her bid-per-click and her daily budget. Per-item values and overall budgets model well how many people make decisions in auctions with lots of items, especially when the items are identical.