Applications of geometry to economics, in auction theory and beyond

Content

1. Introduction to the "locus of indifference prices" (LIP) and the dual "demand complex". (slides)  Definition and equivalent characterisations of "demand types".  Application to combinatorial contract theory.

2.  Existence of competitive equilibrium with indivisible goods (slides): the problem, and the characterisation of many transferable utility cases provided by the unimodularity theorem.  Extension to settings with income effects via the "equilibrium existence duality".

3. The Product-mix auction: theory and applications.  

4. Application to matching with transferable utility, and strategy proof mechanisms.

References

• Elizabeth Baldwin and Paul Klemperer.  "Tropical geometry to analyse demand".  Working paper (2014) available https://elizabeth-baldwin.me.uk/papers/baldwin_klemperer_2014_tropical.pdf

• Elizabeth Baldwin and Paul Klemperer. "Understanding Preferences: "Demand Types", and the Existence of Equilibrium with Indivisibilities." Econometrica, Volume 87, Number 3 (May, 2019) Pages 867-932. DOI:10.3982/ECTA13693 

•  Elizabeth Baldwin, Ravi Jagadeesan, Paul Klemperer and Alex Teytelboym.  "On Consumer Theory with Indivisible Goods".  Preprint (2021) available https://elizabeth-baldwin.me.uk/papers/consumer-theory-indivisible.pdf

• Elizabeth Baldwin, Ravi Jagadeesan, Paul Klemperer and Alex Teytelboym. "The Equilibrium Existence Duality". Journal of Political Economy, Volume 131, Number 6, Pages 1440-1476, 2023. DOI:10.1086/722935

•  Elizabeth Baldwin, Paul Goldberg, Paul Klemperer and Edwin Lock. "Solving Strong-Substitutes Product-Mix Auctions". Mathematics of Operations Research, Volume 49, Issue 3, pages 1303-2047 (2024). https://doi.org/10.1287/moor.2019.0248

•  Elizabeth Baldwin, Martin Bichler, Maximilian Fichtl and Paul Klemperer. "Strong Substitutes: Structural Properties, and a New Algorithm for Competitive Equilibrium Prices".  Mathematical Programming, Volume 203, pages 611–643, (2024). DOI:10.1007/s10107-022-01792-w

•  Elizabeth Baldwin, Paul Klemperer and Edwin Lock. "Implementing Walrasian Equilibrium---the Language of Product-Mix Auctions"  Preprint (2024) available https://elizabeth-baldwin.me.uk/papers/PMAlanguages.pdf

• Elizabeth Baldwin, Paul Duetting, Michal Feldman and Maya Schlesinger. "Combinatorial Contracts Through Demand Types".   ACM Conference on Economics and Computation (2026); Arxiv preprint https://arxiv.org/abs/2604.15125 (2026)

•  Keisuke Bando, Kenzo Imamura, Tomoya Kazumura and Elizabeth Baldwin. "Strategy-proofness and competitive equilibrium with transferable utility: The necessity of gross substitutes".  In preparation.

• Robert Crowell and Ngoc Mai Tran. "Tropical geometry and mechanism design" arXiv preprint arXiv:1606.04880

• Marzena Rostek and Nathan Yoder. "Complementarity in Matching Markets and Exchange Economies".  Games and Economic Behavior, 150: 415-435 (2025)

• Marzena Rostek and Nathan Yoder. "Matching with Complementary Contracts" Econometrica, 88 (5): 1793-1827 (2020)

• Ngoc Mai Tran and Josephine Yu, "Product-Mix Auctions and Tropical Geometry", Mathematics of Operations Research, Volume 44, Issue 4 (November 2019) Pages 1145-1509, C2