A coauthored thread: A lot has been said about the #NobelPrize2020 of Milgrom & Wilson, but @ShengwuLi and I would like to say a bit more. As two of Paul’s recent students, here’s our perspective on why auction theory is at the core of economic thinking. 1/14

A central hypothesis in economics is that markets can gather information to coordinate production and consumption. As Hayek (1945) argues, they make use of “knowledge which is not given to anyone in its totality”. When (if at all) is this possible? 2/14

In the 1950s, Arrow, Debreu, and Hurwicz gave a beautiful answer. In a series of blockbuster papers, they established the existence of competitive equilibrium (CE) prices and showed that under some conditions those prices are unique. 3/14

In particular, "On the stability of the competitive equilibrium" by Arrow-Hurwicz showed that gross substitutability guarantees the uniqueness of CE prices and showed that a simple dynamic process leads to the fixed point of CE prices. This "tatonnement" process is: 4/14

"Fix a set of prices. For each good see if there's excess demand/supply. Increase prices for goods in excess demand & decrease for goods that are in excess supply. Stop changing when all goods are in supply=demand." 5/14

Thus, markets can aggregate information through prices, and they can also discover prices by adjusting based on supply and demand. This, in a sense, formalizes Adam Smith’s idea of the “invisible hand.” 6/14

This was an incredible result! Except for the fact that: (1) it assumed agents are price-takers, implicitly a large market (2) it wasn't concerned with strategic incentives, (3) it assumed goods are divisible, & (4) it assumed computation and communication is easy. 7/14

Auction theory asks a fundamental question: How do public prices come to reflect private information? Why would strategic agents interact with the price system in a way that reveals what they know? How can we create systems that make this happen? How can we discover prices? 8/14

Auction theorists’ answers to these questions clarified that the invisible hand of the market is invisible because it’s often not there: Left on their own, markets can fail to discover prices for a variety of reasons. To overcome this requires design. 9/14

The “simultaneous multiple round auction" (SMRA) that's mentioned in the Nobel article is indeed an adaptation of Arrow-Hurwicz's "price discovery" process for a setting with a few mobile broadband firms, who have private info, and an indivisible good (radio spectrum). 10/14

SMRA is a success, but it’s not applicable to all allocation problems. Indeed, that’s the big lesson of market design: it teaches us that the devil is in the details; price discovery fails for a variety of reasons, and thus we need a variety of designs to address them. 11/14

In fact, while Milgrom & Wilson’s research was mainly focused on issues of information and incentives, Paul’s recent work has largely focused on price discovery in a world with computational and communication complexities, standing on the shoulders of computer scientists. 12/14

For instance, the 2017 FCC Incentive Auction for radio spectrum faced physical constraints that were far more complex than those that came before. Checking whether a given assignment was even legally feasible turned out to be NP-complete. 13/14

This led to the development of novel algorithms, with the help of Kevin Leyton-Brown, a computer scientist.

Some great sources on Econ-CS challenges, Paul’s book, “Discovering Prices”, @jasondhartline's “approximate mechanism design”, and @algo_class LectureNotes. 14/14