Keywords: indivisible goods, competitive equilibrium, pseudomarkets, convexity, duality, income effects, net substitutes, budget constraints.
Organizers: Ravi Jagadeesan (Stanford University), and Alex Teytelboym (University of Oxford)
Format: 2 hours with two 45-minute sessions with 15 mins for questions.
Abstract: Accounting for indivisibilities is important in applications of price theory, such as auctions and matching markets. There has recently been a flurry of research on the analysis of equilibrium in markets for indivisible goods. The proposed tutorial will present and synthesize the latest developments in our understanding of how to handle indivisibilities in consumer theory and equilibrium analysis. We plan to cover new work on transferable utility economies, economies with income effects, and pseudomarkets.
Detailed outline:
Lecture 1 (Jagadeesan, 2-3pm ET 25 June 2024):
- Exchange economies with transferable utility (TU)
- Equilibrium existence under (gross) substitutes
- Complementarities and the economics of convexity with indivisible goods
Lecture 2 (Teytelboym, 3-4pm ET 25 June 2024):
- Exchange economies with income effects and the equilibrium existence duality
- Pseudomarket model
- Equivalence between pseudomarket equilibria and equilibria in TU economies
The main papers we plan to cover are:
- Baldwin, E., R. Jagadeesan, P. Klemperer, and A. Teytelboym (2023). The Equilibrium Existence Duality. Journal of Political Economy 131(6), 1440-1476.
- Jagadeesan, R. and A. Teytelboym (2024). The Economics of Equilibrium with Indivisible Goods. Working paper.
- Nguyen, T. and A. Teytelboym (2024). Equilibrium in Pseudomarkets. EC’24
To make the tutorial as accessible as possible, we also plan to cover some background material from the following papers:
- Budish, E., Y.-K. Che, F. Kojima, and P. Milgrom. Designing Random Allocation Mechanisms: Theory and Applications. American Economic Review 103(2), 585-623.
- Gul, F., W. Pesendorfer, and M. Zhang (2022). The Efficient Allocation of Indivisible Goods. Forthcoming at the Journal of Political Economy.
- Gul, F. and E. Stacchetti. Walrasian Equilibrium with Gross Substitutes. Journal of Economic Theory 87(1), 95-124.
- Hylland, A., and R. Zeckhauser (1979). The Efficient Allocation of Individuals to Positions. Journal of Political Economy 8(2), 293-314.
- Hatfield, J. W., S. D. Kominers, M. Ostrovsky, A. Nichifor, and A. Westkamp (2013). Stability and Competitive Equilibrium in Trading Networks. Journal of Political Economy 121(5), 966-1005.
- Hatfield, J. W., S. D. Kominers, M. Ostrovsky, A. Nichifor, and A. Westkamp (2019). Full Substitutability. Theoretical Economics 14(4): 1535-1590.
- Kelso, A. S. and V. P. Crawford (1982). Job Matching, Coalition Formation, and Gross Substitutes. Econometrica 50(6), 1483-1504.
- Nguyen, T. and R. Vohra (2021). (Near-)Substitute Preferences and Equilibria with Indivisibilities. Forthcoming at the Journal of Political Economy.
- Weinstein, J. (2022). Direct Complementarity. Working paper.
Goals, Importance, and Timeliness: The goal of the proposed tutorial is to provide a unified overview of some of the recent developments in the literature on equilibrium with indivisible goods in a variety of important economic settings. We also plan to highlight connections to classical analyses of preferences in economics, and introduce participants trained in computer science and operations research to these concepts. The theory has numerous important applications in spectrum auctions, course assignment, and the allocation of food to food banks. The proposed tutorial is especially timely since the papers it is based on have been written in the last couple of years. We hope that expositing the connections between different economies and equilibrium concepts using familiar mathematical tools will encourage further research in this area.
Target Audience: Graduate students, postdocs, and faculty, as well as advanced undergraduates, in computer science, economics, and operations research.
Prerequisites: Knowledge of microeconomic theory at the introductory graduate level.