Economics might be the realm of money, but economists also study “markets” in which money is not used. When a university course has more interested students than available seats, how does the school decide which students are admitted to those courses? How does a food charity allocate truckloads of donations among its food banks? These, and many other items that are distributed without the use of real currency, are the domain of economists who study these non-monetary markets, which are known as “pseudomarkets.”

 

Economists have developed robust ways to determine when a market that does use money has equilibrium prices; that is, when prices exist that will balance supply and demand. The case of pseudomarkets, on the other hand, is not as well developed. 

 

Alexander Teytelboym, an economist at the University of Oxford, focused on the use of pseudomarkets to allocate so-called indivisible goods, such as university courses, at the Simons Laufer Mathematical Sciences Institute in fall 2023. The program he attended, Mathematics and Computer Science of Market and Mechanism Design, welcomed researchers working at the intersection of economics, mathematics, and computer science to investigate a variety of questions related to understanding what incentives and mechanisms lead to market mechanisms with desirable features.

 

Teytelboym, with coauthor Thành Nguyen of Purdue University Daniels School of Business, discovered that markets and pseudomarkets are more intimately related than economists had previously realized. “To economists, they look like pretty different problems,” Teytelboym says. Participants in markets have effectively limitless budgets of real money and outcomes are deterministic, while in pseudomarkets, participants have limited budgets of tokens and their outcomes could be determined by lottery. “The techniques you use to analyze them are completely different,” he says. Questions about markets would usually use integer linear programming, while pseudomarkets require additional tools such as topological fixed-point theorems. But Teytelboym and Nguyen proved that the existence of solutions to finding equilibrium prices in one case implies solutions in the other.

Photo Credit: Alameda County Community Food Bank via Flickr (CC BY-ND 2.0)

Whether equilibria exist in a market often depends on whether the goods in a market are substitutes for each other or complements. For example, coffee and tea could be substitute goods for some consumers, so when coffee prices rise, consumers may buy less coffee and more tea. On the other hand, if coffee prices rise, people will probably buy less of both coffee and cream. Those goods are likely to be complements. Teytelboym and Nguyen found that in both markets and pseudomarkets, the existence of equilibria depends on the same conditions on whether goods are substitutes or complements. “That was a nice addition to our stock of knowledge,” Teytelboym says, because it meant that they could take more established insights from markets and apply them to pseudomarkets.

 

The interdisciplinary reach of the Market and Mechanism Design program made SLMath a fruitful place for new insights. “I think it was critical that there were people who were highly mathematically trained and were approaching similar questions from different disciplines,” Teytelboym says. “It was amazingly enriching to get ideas from people in other fields who studied similar problems using different training and tools.”

Evelyn Lamb