Duality in Market Design: Theory and Applications

Project Information

DUALMARKETS

Grant agreement ID: 949699

DOI

10.3030/949699

EC signature date 28 September 2020

Start date 1 July 2021

End date 30 September 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 060 381,00

EU contribution

€ 1 060 381,00

Coordinated by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom

Periodic Reporting for period 2 - DUALMARKETS (Duality in Market Design: Theory and Applications)

Reporting period: 2023-01-01 to 2024-06-30

Summary of the context and overall objectives of the project

What is the problem/issue being addressed?
Market design uses economic theory to improve the function of real-world marketplaces, such as matching systems and auctions. In many markets, participants trade goods which are indivisible and highly heterogeneous. My focus is on settings in which participants also experience “income effects”. Income effects arise when participants face budget constraints or when transactions substantially affect participants’ wealth. Income effects are present in many important markets: from spectrum licenses and airport landing slots to jobs and houses. But designing well-functioning marketplaces for participants who experience income effects is challenging both in theory and in practice. As a result, income effects are often ignored in marketplace design, leading to unfair and inefficient outcomes.
The goal of DUALMARKETS is to understand how to design fair and efficient marketplaces for participants with diverse preferences and income effects. Marketplaces work well when supply equals demand and when participants cannot improve their outcomes by renegotiating. I will develop new tools to incorporate income effects into many marketplaces, including matching markets and auctions.

Why is it important for society?
Market design uses economic theory to improve the function of real-world marketplaces, such as matching systems and auctions (Kominers et al., 2017). There are many prominent examples of successful market design including matching doctors to hospital residencies (Roth, 1984), auctioning radio spectrum to telecoms (Binmore and Klemperer, 2002; Milgrom and Segal, 2018), allocating children to schools (Abdulkadirog ̆lu and Sönmez, 2003), assigning students to business school courses (Budish, 2011), and distributing food donations to food banks (Prendergast, 2017). Other projects I have been involved in include redesigning systems for resettlement of refugee families (Delacrétaz et al., 2023; Trapp et al., 2021), auctions for fishing quota (Laksá et al., 2018), energy trading (Morstyn et al., 2018), allocation of social housing, and matching school leavers to university places.
To design a well-functioning marketplace, it is crucial to know when the market works well. Markets typically work well when supply equals demand. In markets for commodities, such as wheat or oil, prices that clear markets always exist and are easy to find. But in many markets, goods are highly heterogeneous and indivisible. Consider radio spectrum licenses: when they are auctioned to telecoms, licenses are sold in indivisible license bands. But licenses are also highly heterogeneous: some licenses cover more populated geographical areas, others are only valuable in contiguous blocks. As a result, there is no single market price for radio spectrum, but a different market price for each different spectrum license band. Organising marketplaces for heterogeneous indivisible goods is challenging: it might not be possible to find prices that equate supply to demand in all the markets. And, without equilibrium, market outcomes can be “unstable” as participants seek to recontract and do side-deals. Good marketplace design therefore brings substantial gains for society by allocating scarce resource more efficiently and more fairly.

What are the overall objectives?
DUALMARKETS will expand our understanding of marketplaces for heterogeneous indivisibilities where income effects are present, thereby vastly extending the power and applicability of market design tools. DUALMARKETS has three specific Objectives. Objectives 1 and 2 focus on new theoretical foundations for market design. Objective 1 identifies novel conditions under which competitive equilibrium exists in markets with heterogeneous indivisibilities. Objective 2 connects competitive equilibrium to the “stability” of market outcomes. Objective 3 is applied: it uses insights from the first two Objectives to suggest designs of auctions in which participants experience income effects.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Thus far, we have made progress in two ways.

First, we developed what we called the “Equilibrium Existence Duality”. This analytical result elegantly connects markets with and without income effects. In particular, it allows one to easily check whether a marketplace is likely to guarantee market-clearing. To do so, the Equilibrium Existence Duality allows one to “take out” income effects, check whether markets clear in a related economy without income effects (which is easy), and, if they do, “put back” the income effects while guaranteeing that markets will still clear. This result dramatically improved and expanded our understanding of when and how market clear: in fact, our Equilibrium Existence Duality allows us to generate new economies in which markets always clear and give both necessary and sufficient conditions for equilibrium existence.

Second, we applied the insights from the “Equilibrium Existence Duality” to two-sided matching markets in which there are sellers on one side and buyers on the other. We also considered what happens when buyers can completely run out of money (what is known as a “hard” budget constraint.) We showed many fascinating results about the existence of outcome which are robust to renegotiation (known as “stable” outcomes) even though markets typically do not clear exactly in this setting. Results from this paper called “Matching and Prices” can be used to understand the design of many two-sided markets including auctions.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Prior to this project, much was known about the possibility of market-clearing with indivisible goods, but without income effects. Little was understood when income effects were present. With our Equilibrium Existence Duality, we have been able to bring the understanding of market-clearing economies with income effects to the same level as those without. This dramatically expanded what was thought to be possible. In particular, we showed for the first time that market-clearing is perfectly possible (or stable outcomes can be found) when some agents view goods as (gross) substitutes and others as (gross) complements. This constitutes an important step in connecting work in market design to the older and foundational work on general equilibrium theory.

In the rest of the project, we are planning to apply these insights more specifically to auction design, to the complexity of computing equilibrium outcomes, and to the design of marketplaces where outcomes can be randomized. First, we want to understand what bidding languages allow auctions with budget constraints clear approximately. Second, we want to understand how challenging it might to be compute market-clearing prices when income effects are present and whether there are special cases when it is computationally efficient. Third, we want to explore further dualities between economies without income effects and economies in which agents can trade probability shares of receiving items.