EQUIPRICE papers

The following papers benefited from the support of the ERC-sponsored project EQUIPRICE.

Working papers

Stable and extremely unequal. With Octavia Ghelfi and Marc Henry. Manuscript available on arxiv.

Published or forthcoming papers

Yogurts choose consumers? Identification of Random Utility Models via Two-Sided Matching. With Odran Bonnet, Yu-Wei Hsieh, Keith O’Hara, and Matt Shum. Forthcoming, Review of Economic Studies. Available here.
A note on the estimation of job amenities and labor productivity. With Arnaud Dupuy. Forthcoming Quantitative Economics. Available here.
Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models. With Bernard Salanié. Forthcoming, Review of Economic Studies. Available here.
SISTA: learning optimal transport costs under sparsity constraints. With Guillaume Carlier, Arnaud Dupuy and Yifei Sun. Accepted for publication, Communications on Pure and Applied Mathematics. Available here.
On the representation of the nested logit model. Accepted for publication, Econometric Theory. Available here.
Single market nonparametric identification of multi-attribute hedonic equilibrium models. With Victor Chernozhukov, Marc Henry, and Brendan Pass. Accepted for publication, Journal of Political Economy. Available here.
Fritz John’s equation in mechanism design (2021). Economic Theory Bulletin 9, pp. 1–5. Available here.
Taxation in matching markets. With Arnaud Dupuy, Sonia Jaffe, and Scott Kominers. Forthcoming, International Economic Review. Available here.

EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing. European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025.

EQUIPRICE code

TraMEPy Project

The TraME software (Transportation Methods for Econometrics, http://www.trame-project.com/) is a collection of libraries for solving problems of equilibrium computation and estimation in consumer demand and matching frameworks via the Mass Transportation Approach. It will be completely revamped to accommodate for the equilibrium flow problem in its full generality (beyond bipartite networks), novel equilibrium algorithms added, enhanced HPC capabilities, and a new Python implementation.

EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing. European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025.

EQUIPRICE scientific agenda

The EQUIPRICE project seeks to build an innovative economic toolbox (ranging from modelling, computation, inference, and empirical applications) for the study of equilibrium models with gross substitutes, with applications to models of matching with or without transfers, trade flows on networks, multinomial choice models, as well as hedonic and dynamic pricing models. While under-emphasized in general equilibrium theory, equilibrium models with gross substitutes are very relevant to these problems as each of these problems can be recast as such.
Thus far, almost any tractable empirical model of these problems typically required making the strong assumption of quasi-linear utilities, leading to a predominance of models with transferable utility in applied work. The current project seeks to develop a new paradigm to move beyond the transferable utility framework to the imperfectly transferable utility one, where the agent’s utilities are no longer quasi-linear.
The mathematical structure of gross substitutes will replace the structure of convexity underlying in models with transferable utility.
To investigate this class of models, one builds a general framework embedding all the models described above, the “equilibrium flow problem.” The gross substitute property is properly generalized and properties (existence of an equilibrium, uniqueness, lattice structure) are derived. Computational algorithms that rely on gross substitutability are designed and implemented. The econometrics of the problem is addressed (estimation, inference, model selection). Applications to various fields such as labor economics, family economics, international trade, urban economics, industrial organization, etc. are investigated.
The project touches upon other disciplines. It will propose new ideas in applied mathematics, offer new algorithms of interest in computer science and machine learning, and provide new methods in other social sciences (like sociology, demography and geography).

Seven scientific challenges

Challenge 1. How to build a single framework to be able to reformulate matching models with or without (or with imperfect) transfers, hedonic models, models of multinomial choice, and models of international trade as problems of competitive equilibrium with gross substitutes?

Challenge 2. How to extend the framework investigated in challenge 1 to handle dynamic, Markov versions of these problems (both in the finite-horizon and stationary case)?

Challenge 3. How to extend the notion of gross substitutes to allow for the possibility of indifference between preferred alternatives, i.e. consider the case of set-valued excess demand / supply?

Challenge 4. Build and analyze a set of algorithms for the equilibrium problem with gross substitutes to handle the problems described in the previous Challenges.

Challenge 5. Implement these algorithms into a compiled, parallelized software library.

Challenge 6. Develop a novel inferential theory based on minimax regret estimation for the estimation of equilibrium models with Gross Substitutes, to handle inference in the previous problems.

Challenge 7. In the minimax regret estimation framework of challenge 6, extend the estimation and inference theory to handle sparsity constraints.

EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing. European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025.

EQUIPRICE positions

Open positions

Post-doctoral researcher (TBA)

The post-doctoral researcher will be expected to contribute to the intellectual advancement of the project, interact with the PhD students, and participate in the organization of the seasonal events described below. The post-doctoral position is envisioned for four years; however, depending on individual circumstances, it may also be two consecutive two-year positions.

Two doctoral fellows

One doctoral fellow will have a focus on computational economics. The other doctoral fellow will focus on empirical economics.

Research assistants

March 14, 2021: Equiprice is looking for an intern in the field of data science and economics.

EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing. European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025.

EQUIPRICE workshops

Upcoming workshops

Fall 2021: Workshop on optimal transport with applications to economics and statistics, blended, Sciences Po, Paris.

EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing. European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025.

EQUIPRICE lectures

Upcoming lectures

February 26 2021, 2pm-4pm (Paris time): estimation of dynamic discrete choice problems

Speaker: Alfred Galichon

• Theory: Rust’s model; estimation; normalization issues
• Coding: maintenance choice.

March 12 2021, 2pm-4pm (Paris time): matrix games

Speaker: Alfred Galichon

• Theory: Nash equilibria; correlated equilibria; zero-sum games and LP formulation
• Coding: soccer data on penalty.

April 9 2021, 2pm-4pm (Paris time): kidney exchange problems

Speaker: Jules Baudet.

• Theory: Roth et al.
• Coding: an interactive multi-player simulator

Special lecture 5 (April 30, 2pm-4pm Paris time): traffic congestion

Speaker: Alfred Galichon

• Theory: Wardrop equilibria; price of anarchy
• Coding: traffic data.

Past lectures

February 5 2021, 2pm-4pm (Paris time): cloud computing

Speakers: Flavien Léger (Equiprice) and James Nesbit (NYU).

EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing. European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025.

EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing

European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025

CORE Equiprice team

Principal investigator:

Postdoctoral researchers:

Research assistants:

EQUIPRICE lunch seminars

Equiprice lunch seminars are hybrid (in person and / or virtual, depending on the COVID context) lunch seminars designed to serve as technical tutorials or presentation of work in progress in relation to the scientific agenda of the ERC-sponsored project EQUIPRICE. Unless noted ‘internals,’ seminars are public and open to all, but registration to the in person event is required 48 hours before.

Note: All times indicated on this page refer to the Paris time zone.

Upcoming talks:

• May 19 2022, 12pm-1pm (online), Dr. Adrian Vladu (IRIF) will present TBA.
  Show Press Release (2 More Words)
  Abstract: TBA.

Past talks:

• February 10 2022, 12pm-1pm (online), Mert Unsal (Ecole Polytechnique) will present ‘running C++ on jupyter notebook: the xeus cling kernel’.
  Show Press Release (2 More Words)
  Abstract: TBA.
• February 3 2022, 12pm-1pm (online), Professor Claire Mathieu (CNRS, Irif) will present “Stable Matching in Practice”.
  
  Show Press Release (163 More Words)
  Abstract: Stable matching methods, based on the algorithm designed by Gale and Shapley, are used around the world in many applications such as college admissions. Several criteria measure the quality of the result: number of students assigned; rank of the college assigned to the applicant in their preference list; robustness; running time; etc.
  After reviewing properties of the algorithm in the pure, ideal setting, we present issues arising in practice. The input data is uncertain and evolves with time, so a one-shot algorithm does not suffice. It is not feasible for admission committees to meet continuously, so the process cannot be fully dynamic. To reconcile those competing constraints, a hybrid implementation proceeding partly online on the student side was recently proposed for college admissions in France.
  Finally, after remarking that the men-optimal stable matching and the women-optimal stable matching are almost identical, we propose a probabilistic model for highly correlated preferences to provide a theoretical explanation.
  This is joint work with Hugo Gimbert and Simon Mauras.

• ***Wednesday*** January 12 2022, *** 2pm-3pm *** (online), Dr. Antoine Jeanjean (OPT2A) will present “Operations research: a love story between mathematics and computer science.”
  Show Press Release (70 More Words)
  Abstract: From the optimization of highway planning to the minimization of formwork stocks on construction sites, through the optimization of the planning of advertising screens, Operations Research is a discipline that deals with the development of advanced analytical methods to improve decision-making. We will illustrate the discipline through concrete examples from real projects and we will also present some methods and tools used to solve them, in particular local search.
• December 16 2021, 12pm (online), Dr. Denis Merigoux (INRIA) will present “Turning law into micro-simulation code with the Catala programming language”.
  
  Show Press Release (121 More Words)
  Abstract: Software called legal expert systems are used around the world by private and public organizations to compute taxes. A bug in such programs can lead to tax miscalculations and heavy legal and democratic consequences. Yet, increasing evidence suggests that some legal expert systems may not meet satisfying criteria to be in compliance with the law. Moreover, they are difficult to adapt to the continuous flow of new legislation just by using traditional software development processes. To prevent further software decay and reconcile these systems with the growing demand for algorithmic transparency and economic micro-simulation of reform impact, we present a solution built by lawyers and computer scientists : a new programming language, Catala, coupled with a pair programming development process.

• December 9 2021, 12pm (online), Anatole Gallouet (Grenoble INP) will present “Numerical resolution of semi-discrete Generated Jacobian equations”.
  
  Show Press Release (160 More Words)
  Abstract: In non-imaging optics, we try to optimize the trajectory of the light from a source to a target without trying to form an image of the source on the target. Some non-imaging optic problems can be translated into optimal transport problems in a semi-discrete setting, meaning that the source is a continuous domain and the target is a finite set of points. Other problems of non-imaging optics can sometimes be rewritten into a slightly more global form than optimal transport, which we call Generated Jacobian Equations. During this presentation we will focus on these Generated Jacobian Equations, also in a semi-discrete setting. We will begin by introducing them using a non-imaging optic problem, and make the link with optimal transport. We will then present an algorithm to solve Generated Jacobian Equations, which was adapted from an existing algorithm to solve optimal transport problems. And finally we will detail the main lines of the proof of convergence of this algorithm.

• November 25 2021, 12pm (hybrid), Professor Benoit Rottembourg (INRIA) will present “Dynamic pricing: constraints, elasticity and algorithmic manipulation”. 
  
  Show Press Release (204 More Words)
  Abstract: Dynamic pricing was popularized in the 1980s by the U.S. airline industry, in the midst of deregulation. It consisted above all in filling the aircraft, by optimizing the fare mix under capacity constraints. However, the customer’s vision was very crude; this was before the Internet era and it was the travel agent who was in charge of the search and booking. The same techniques, based on customer segmentation, demand forecasting and (stochastic) mix optimization, have been successfully propagated to other market sectors such as rail transport, cruises, hotels or even very recently container transport.
  In this presentation, we will aim at showing how dynamic pricing as applied by large digital platforms (market places, online travel agencies, etc.) offers a breakthrough in the way of anticipating and influencing customer behavior through price. We will insist on the fact that this power of influence, boosted by new families of algorithms, is powerful but can generate abuses. These abuses may concern consumers’ law, suppliers’ rights and potentially competition law. We will try to show the difficulties to audit this kind of practices and the challenges for the regulatory authorities. We willargue for new supervisory frameworks, as outlined in the Digital Market Act proposals at the European level.
• November 18 2021, 12pm (hybrid). Professor César Ducruet (Paris-Nanterre University) will present “Inter-city networks: a maritime perspective”.
  Show Press Release (167 More Words)
  Abstract: Although more than 80% of world trade volumes occur by sea, and about 60% of world urban population is coastal, no previous research has been done on how cities are linked by maritime flows. Based on untapped shipping records and population data, we construct a global network with cities as nodes and inter-port vessel voyages as links. The first part of the analysis looks at the evolution of traffic concentration and port-city correlation since the late nineteenth century. While the largest cities kept concentrating traffic in a stable manner, the correlation gradually lost in significance. The latter trend, however, varied according to the type of location and the level of observation.
  The second part on the maritime connectivity of cities confirms the overwhelming importance of city size, but sheds more light on the shift of hub functions towards pivotal ports and from Atlantic to Asia-Pacific. A spatial interaction model shows that the network obeys gravitational properties, as larger cities connect more with each other,
  but less at distance.
• October 7, 2021. Reading of Roth,  Rothblum and Vande Vate’s Stable Matchings, Optimal Assignments, and Linear Programming.
• September 12 2021, 12:30pm. Pauline Corblet’s job market paper’s practice talk.
• July 15 2021, 1pm. Loan Tricot on Bertsekas’ auction algorithm.
• ***WEDNESDAY*** June 23 2021, ***12.30pm-2pm***. Pauline Corblet. Job market practice talk.
• June 17, 1pm. Loan Tricot on “Reconstructing the order flow with optimal transport”.
  Show Press Release (195 More Words)
  Abstract: Exchanges receive three types of orders:

  • Limit orders, making liquidity
  • Market orders, taking liquidity
  • Cancel orders, taking liquidity

  Limit orders are standing offers to buy (sell) a defined amount at a defined price. They can be cancelled using Cancel orders. Market orders are orders to buy a defined amount at market price: the best price which can be achieved using standing offers. Limit orders are accumulated and aggregated into a tick level order book, which contains the size of aggregated standing offers at each price. Market orders trigger one or more trades when they are matched with one or more Limit orders. Exchanges stream the order book updates and the trades flow to market participants, but never stream the order flow. Order book updates and trades are usually not aligned (w.r.t. time) and sometimes presented in aggregate form. The large number of, and lack of standardization between, (crypto) exchanges means there are no guarantees concerning the quality of the data. The order flow is valuable data which can be used to study agents’ behavior on the market, and possibly design algorithmic trading strategies. We attempt to reconstruct the order flow from the order book updates and trades flow.

• June 3 2021, 1pm. Bastien Patras on BLP and MPEC.
• *** Tuesday*** May 25 2021, 1pm. Reading of The Contraction Mapping Approach to the Perron-Frobenius Theory: Why Hilbert’s Metric?.
• May 20 2021, 1pm (public). Professor Guillaume Carlier (Paris-Dauphine University), on “the linear convergence of the multi-marginal Sinkhorn algorithm.”
• April 29 2021, 1pm. Reading of Bubeck and Cesa-Bianchi’s Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems  chapters 1-3.
• April 15 2021, 1pm. Flavien Léger on Bregman divergence and gradient descent (part 2).
• April 8 2021, 1pm. Flavien Léger on Bregman divergence and gradient descent (part 1).
• March 25 2021, 1pm. Pauline Corblet on the link between Gale and Shapley and some iterative methods in applied mathematics.
• March 18 2021, 1pm. Jules Baudet on course allocation mechanisms (continued).
• March 4 2021, 1pm. Pauline Corblet on many-to-one matching problems.
  Show Press Release (2 More Words)
  Abstract: TBC.
• February 18 2021, 1pm (public). Jules Baudet on course allocation mechanisms (continued).
  Show Press Release (5 More Words)
  Abstract: Continued from Jan 7.
• February 11 2021, *** 5pm *** (public). Professor Xin Chen (University of Illinois) on S-convexity.
  Show Press Release (2 More Words)
  Abstract: TBC.
• January 14 2021, 1pm (public). Flavien Léger on Chambolle-Pock.
  Show Press Release (3 More Words)
  Abstract: TBC.
• January 7 2021, 1pm (public). Jules Baudet on “the multi-unit assignment problem: matching students to course schedules”.
  Show Press Release (169 More Words)
  Abstract: In this talk, we will review a series of papers by Eric Budish and his co-authors on the multi-assignment problem, which consists in answering: how to optimally assign bundles of items to agents? In particular, we will study the allocation of course schedules to students.
  First, we will see that traditional optimality criteria used for single-item matching are difficult to extend to combinatorial settings by looking at the flaws of the Harvard Course Allocation mechanism. Then, we will introduce the A-CEEI mechanism which offers better fairness, strategyproofness and efficiency guarantees.
  The reference papers for this talk are:
  – Budish, E. (2011). The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. Journal of Political Economy, 119(6), 1061-1103.
  – Budish, E., & Cantillon, E. (2012). The multi-unit assignment problem: Theory and evidence from course allocation at Harvard. American Economic Review, 102(5), 2237-71.
  – Budish, E., Cachon, G. P., Kessler, J. B., & Othman, A. (2017). Course match: A large-scale implementation of approximate competitive equilibrium from equal incomes for combinatorial allocation. Operations Research, 65(2), 314-336.
• December 10 2020, *** 5pm *** (public). Professor Pierre-Olivier Weill (UCLA) on optimal transport in asset pricing problems.
  Show Press Release (121 More Words)
  The talk will be based on the paper “Incentive Constrained Risk Sharing, Segmentation, and Asset Pricing” with Bruno Biais and Johan Hombert.
  Abstract: Incentive problems make securities’ payoffs imperfectly pledgeable, limiting agents’ ability to issue liabilities. We analyze the equilibrium consequences of such endogenous incompleteness in a dynamic exchange economy. Because markets are endogenously incomplete, agents have different intertemporal marginal rates of substitution, so that they value assets differently. Consequently, agents hold different portfolios. This leads to endogenous markets segmentation, which we characterize with Optimal Transport methods. Moreover, there is a basis going always in the same direction: the price of a security is lower than that of replicating portfolios of long positions. Finally, equilibrium expected returns are concave in factor loadings.
• November 26 2020, 1pm (public). Flavien Léger on computing large-scale regularized optimal transport problems.
  Show Press Release (14 More Words)
  Abstract: We shall describe some aspects of handling large scale problems, in Python.
• November 12 2020, 1pm. Alfred Galichon on ‘EQUIPRICE: research program and challenges’.
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  Abstract: In this talk, I will outline the broader research program of EQUIPRICE, and I will describe some scientific challenges and some projects for EQUIPRICE in 2020-2021.
• October 29 2020, 1pm (public). Jules Baudet will be presenting on ‘Cloud Computing and Containers part 3: Understanding Docker containers, continued’.
• October 22 2020, 1pm (public). Jules Baudet will be presenting on ‘Cloud Computing and Containers part 2: Understanding Docker containers’
  Show Press Release (55 More Words)
  Abstract: In this second session (continued from part 1), we will demonstrate how to create a Virtual Machine on Google Cloud, on which we will deploy a container containing Jupyter notebooks. We will also show how to access and run these notebooks. We will conclude by comparing Google Colab to Google Cloud for running notebooks.
• October 15 2020, 1pm (public). Jules Baudet on kidney exchanges.
  Show Press Release (182 More Words)
  Abstract: Re-organizing the French Kidney Exchange Program
  Jules BAUDET
  Market Design is an area of Economics that leverages Game Theory, Experimental Economics and Algorithms to fix market failures by proposing implementable solutions. In 2012, Alvin Roth received the Nobel Prize for his work, in which he studied and helped fix essential matching markets (doctors residency match, school seats allocation…). One of his most famous work is the design of a Kidney Paired Donation Program, allowing to overcome Patient-Donor incompatibilities by exchanging donors between pairs. In this talk, we will analyze and propose solutions to the operational challenges faced by the French Agency for Biomedicine in creating a successful Kidney Paired Donation (KPD) Program. We will study the impact of parameters such as patient priority criteria, size constraints on exchanges and frequency of match runs on the total number of grafts. This talk will underline the dynamic tradeoffs at stake in designing a KPD program, and the importance of conducting regular simulations to adapt the organization of the program to the structure of its pool of participants.
  This talk will be based on the following paper.
• October 8 2020, 1pm (public). Flavien Léger on ‘The back-and-forth method in optimal transport’
  Show Press Release (86 More Words)
  Abstract: For this first lunch seminar we will follow the ‘‘math+econ+code’’ design. We will present the back-and-forth method [1], a recent state-of-the-art algorithm to solve optimal transport problems.
  We will then offer a brief introduction to KeOps [2], an easy-to-use library with a python interface to perform large-scale kernel operations on GPUs. We will implement the back-and-forth method on optimal transport, hedonic equilibrium and equilibrium transport problems.
  [1] Matt Jacobs and Flavien Léger. A fast approach to optimal transport: The back-and-forth method. Numerische Mathematik, 2020. To Appear.
  [2] https://www.kernel-operations.io/keops/index.html
• September 24 2020, 1pm (public). Jules Baudet on ‘Cloud Computing and Containers part 1: Understanding Docker containers’
  
  Show Press Release (175 More Words)
  Abstract: Abstract: This series of talks aims at introducing and showcasing the basic functionalities of Virtual Machines and Docker Containers. Through live demonstrations, we will see how to bundle an application and all of its dependencies in a container before deploying it in the cloud, on a Virtual Machine. In particular, we will show you how to run Jupyter notebooks located inside containers on Virtual Machines. Note: If you would like to follow along during the tutorials, you will need to create a free account on Google Cloud Platform: https://cloud.google.com/?hl=en and to install docker on your computer: https://docs.docker.com/desktop/. In a first session, we will start by introducing Docker containers and comparing them to Virtual Machines. Containers are a technology that revolutionized the computing industry by allowing developers to bundle an application and all its dependencies in a single structure. We will then show how to create, build, and deploy a Docker container. The demonstration will end by sending our Docker Container to Google Cloud Container Registry, in order to be accessible for our following tutorial.

Sponsored by the European Research Council grant EQUIPRICE

European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025

Project description

This project seeks to build an innovative economic toolbox (ranging from modelling, computation, inference, and empirical applications) for the study of equilibrium models with gross substitutes, with applications to models of matching with or without transfers, trade flows on networks, multinomial choice models, as well as hedonic and dynamic pricing models.  Applications to various fields such as labor economics, family economics, international trade, urban economics, industrial organization, etc. are investigated.

This project is hosted by the department of economics at Sciences Po.

The scientific agenda

The EQUIPRICE project is built upon a rigorous scientific agenda at the intersection of economics, data science, mathematics and computation. See here.

Events

EQUIPRICE Lunch Seminars

The EQUIPRICE team meets bimonthly on Thursdays for lunch seminars that hold in person or remotely to discuss research in progress by the team members, or summarize existing research on a topic. Occasionally, an external researcher is invited to present. Some of these meetings are public. See schedule here.

Seasonal events

Winter: ‘math+econ+code’ January masterclass

A ‘math+econ+code’ masterclass is held over one week in the month of January. Topics usually revolve around the economic applications of optimal transport. Find out more information here.

Spring: EQUIPRICE lectures

Topical lectures by EQUIPRICE team members and invited researchers are given during the Spring semester. See a schedule here.

Summer: ‘math+econ+code’ June masterclass

Another ‘math+econ+code’  masterclass is held in June, on a theme which is in general complementary to the January class, typically dealing with Walrasian equilibrium with gross substitutes. More information here.

Fall: EQUIPRICE workshops

A research workshop is organized yearly in the Fall. See a list of past and upcoming workshops here.

EQUIPRICE code & Papers

Open-source code is developed a product of the EQUIPRICE research effort. Find out more here.

Publicly available manuscript version of the papers written with the support of EQUIPRICE are listed here.

The team

The core EQUIPRICE team is made of a principal investigator, post-doctoral researchers, and graduate student assistants. Meet the equiprice team!

Job posting for the EQUIPRICE project are advertised here.

To be added to the ‘math+econ+code’ diffusion list, and to be updated on the upcoming classes, enter your e-mail below: