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.
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.
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.
This very intensive course, part of the ‘math+econ+code’ series, is focused on the computation of competitive equilibrium, which is at the core of surge pricing engines and allocation mechanisms. It will investigate diverse applications such as network congestion, surge pricing, and matching platforms. It provides a bridge between theory, empirics and computation and will introduce tools from economics, mathematical and computer science. Mathematical concepts (such as lattice programming, supermodularity, discrete convexity, Galois connections, etc.) will be taught on a needs basis while studying various economic models. The same is true of computational methods (such as tatonnement algorithms, asynchronous parallel computation, mathematical programming under equilibrium constraints, etc.). Hence there are no prerequisite other than the equivalent of a first-year graduate sequence in econ, applied mathematics or other quantitative disciplines.
The teaching format is somewhat unusual: the course will be taught over five consecutive days, with lectures in the morning and individual assignments in the afternoon. This course is very demanding from students, but the learning rewards are high. The morning lectures will alternate between 1 hour of theory followed by 1 hour of coding. Students are expected to write their own code, and the teaching staff will ensure that it is operational. This course is therefore closer to cooking lessons than to traditional lectures.
Aim of the course
• Provide the conceptual basis of competitive equilibrium with gross substitutes, along with various computational techniques (optimization problems, equilibrium problems). Show how asynchronous parallel computation is adapted for the computation of equilibrium. Applications to hedonic equilibrium, multinomial choice with peer effects, and congested traffic equilibrium on networks.
• Describe analytical methods to analyze demand systems with gross substitutes (Galois connections, lattice programming, monotone comparative statics) and use them to study properties of competitive equilibrium with gross substitutes. Describe the Kelso-Crawford-Hatfield-Milgrom algorithm. Application to stable matchings, and equilibrium models of taxation.
• Derive models of bundled demand and analyze them using notions of discrete convexity and polymatroids. Application to combinatorial auctions and bundled choice.
Instructors
A. Galichon (NYU Econ+Math)
Course material
Course material (lecture slides, datasets, code) will made available before the lectures in this Github repository.
Practical information
• Schedule: June 8-12, 2020. Classes meet 2pm-6pm Paris time / 8am-noon New York time. In addition, supplementary material (approximately 2 hours in length) is made available each day to complement the main lectures.
Part I: Tools
Day 1: Competitive equilibrium with gross substitutes (Monday, 4 hours)
Walrasian equilibrium and gross substitutes. Gradient descent, Newton method; coordinate update method. Isotone convergence and Tarski’s theorem. Parallel computation (synchronous and asynchronous). Fisher-Eisenberg-Gale markets. Hedonic models beyond the quasilinear case.
References:
• Ortega and Rheinboldt (1970). Iterative Solution of Nonlinear Equations in Several Variables. SIAM.
• Heckman, Matzkin, and Nesheim (2010). “Nonparametric identification and estimation of nonadditive hedonic models,” Econometrica.
• Gul and Stacchetti (1999). “Walrasian equilibrium with gross substitutes”. Journal of Economic Theory.
• Jain and Vazirani (2010). “Eisenberg–Gale markets: Algorithms and game-theoretic properties”. Games and Economic Behaviour.
• Cheung and Cole (2016). “A Unified Approach to Analyzing Asynchronous Coordinate Descent and Tatonnement”. Arxiv.
Day 2: Demand beyond quasi-linearity (Tuesday, 4 hours)
Lattices and supermodularity. Veinott’s strong set ordering and Topkis’ theorem; Milgrom-Shannon theorem. Z-maps, P-maps and M-maps. Galois connections and generalized convexity. Equilibrium transport. Models of matching models with imperfectly transferable utility. Stable matchings and Gale and Shapley’s algorithm.
References:
• Veinott (1989). Lattice programming. Unpublished lecture notes, Johns Hopkins University.
• Topkis (1998). Supermodularity and complementarity. Princeton.
• Milgrom and Shannon (1994). “Monotone comparative statics.” Econometrica.
• Rheinboldt (1974). Methods for solving systems of nonlinear equations. SIAM.
• Noeldeke and Samuelson (2018). The implementation duality. Econometrica.
• Kelso and Crawford (1981). Job Matching, Coalition Formation, and Gross Substitutes. Econometrica.
• Roth and Sotomayor (1992). Two-Sided Matching. A Study in Game-Theoretic Modeling and Analysis. Cambdidge.
Day 3: Bundled demand (Wednesday, 4 hours)
Discrete convexity. Lovasz extension; Polymatroids. Hatfield-Milgrom’s algorithm. Combinatorial auctions.
References:
• Fujishige (1991). Submodular functions and optimization. Elsevier.
• Vohra (2011). Mechanism design. A linear programming approach. Cambridge.
• Bikhchandani, Ostroy (2002). The Package Assignment Model”. JET.
• Hatfield and Milgrom (2005). Matching with contracts. AER.
• Danilov, Koshevoy, and Murota (2001). Discrete convexity and equilibria in economies with indivisible goods and money. Mathematical Social Sciences.
Part II: Models
Day 4: Empirical models of demand (Thursday, 4 hours)
Nonadditive random utility models. Strategic complements; supermodular games. Brock-Durlauf’s model of demand with peer effect. Mathematical programming with equilibrium constraints (MPEC).
References:
• Vives, X. (1990). “Nash Equilibrium with Strategic Complementarities,” JME.
• Milgrom and Roberts (1994). “Comparing Equilibria,” AER.
• Berry, Gandhi, Haile (2013). “Connected Substitutes and Invertibility of Demand,” Econometrica.
• Brock, Durlauf (2001). Discrete choice with social interactions. JPE.
• Dubé, Fox and Su (2012), “Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation,” Econometrica.
• Bonnet, Galichon, O’Hara and Shum (2018). Yoghurts choose customers? Identification of random utility models via two-sided matching.
Day 5: Empirical models of matching (Friday, 4 hours)
Distance-to-frontier function, matching function equilibrium. Matching models with taxes. Matching with public consumption. Surge pricing.
References:
• Menzel (2015). Large Matching Markets as Two-Sided Demand Systems. Econometrica.
• Legros, Newman (2007). Beauty is a Beast, Frog is a Prince. Assortative Matching with Nontransferabilities. Econometrica.
• Galichon, Kominers, and Weber (2018). Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility.
Day 6: Equilibrium on networks (Saturday, 4 hours)
Equilibrium on networks. Traffic congestion; Wardrop equilibrium. Braess’ paradox. Price of anarchy.
References:
• Roughgarden, Tardos (2002). How bad is selfish routing? Journal of the ACM.
• Roughgarden (2005). Selfish Routing and the Price of Anarchy. MIT.
• Bourlès, Bramoullé, and Perez‐Richet (2017). Altruism in networks. Econometrica.
• Wardrop (1952). “Some theoretical aspects of road traffic research”. Proc. Inst. Civ. Eng.
• Dafermos (1980). “Traffic Equilibrium and Variational Inequalities.” Transportation Science.
• Nagurney (1993). Network Economics: A Variational Inequality Approach. Kluwer.
Sponsored by:
The National Science Foundation, grant DMS-1716489, “Optimal and equilibrium transport: theory and applications to economics and data science.”
The European Research Council, grant ERC CoG-866274 EQUIPRICE,“Equilibrium methods for resource allocation and dynamic pricing.”
‘math+econ+code’ part one: optimal transport and economic applications
NYU, Courant Institute (Warren Weaver Hall, 251 Mercer) Rm 101, January 20-24, 2020 (30 hours)
Instructor: A. Galichon (NYU Econ+Math). Email: alfred.galichon@nyu.edu. TA: James Nesbit (NYU Econ). Email: jmn425@nyu.edu.
Description
This intensive course, part of the ‘math+econ+code’ series, is focused on models of demand, matching models, and optimal transport methods, with various applications pertaining to labor markets, economics of marriage, industrial organization, matching platforms, networks, and international trade, from the crossed perspectives of theory, empirics and computation. It will introduce tools from economic theory, mathematics, econometrics and computing, on a needs basis, without any particular prerequisite other than the equivalent of a first year graduate sequence in econ or in applied math.
A particular emphasis will be given on HPC computation and parallel computing.
Because it aims at providing a bridge between theory and practice, the teaching format is somewhat unusual: each teaching “block” will be made of 50 minutes of theory followed by 1 hour of coding, based on an empirical application related to the theory just seen. Students are expected to write their own code, and we will ensure that it is operational at the end of each block. This course is therefore closer to cooking lessons than to traditional lectures.
The course is open to graduate students in the fields of economics and applied mathematics, but also in other quantitative disciplines. Students need to bring a laptop with them to the lectures. The knowledge of a particular programming language is not required; students are however expected to have some experience with programming. The language of the course will be Python.
The lecturer is Alfred Galichon (professor of economics and of mathematics at NYU). The TA is James Nesbit (graduate economics student at NYU). Pauline Corblet (graduate economics student at Sciences Po), Octavia Ghelfi and James Nesbit (graduate economics students at NYU) have helped prepare the course material. Support from NSF grant DMS-1716489 is acknowledged.
Suggested preparation readings (optional)
Alfred Galichon (2016). Optimal Transport Methods in Economics. Princeton University Press.
Course material
Available on github here.
Available on NYU’s HPC cluster here.
Course material from past editions available from this Github repository.
Practical information
• Schedule: Monday to Friday, 8:30am-12:30pm and 1:30pm-3:30pm. Location: NYU Courant Institute, Warren Weaver Hall, 251 Mercer St, Room 101.
• Credits: 2, assessed through a take-home exam or a short final paper, at the student’s option.
• A syllabus is available at http://alfredgalichon.com/mec_optim/.
• NYU Students need to register on Albert (code ECON-GA 3503). Students are advised to contact the instructor (alfred.galichon@nyu.edu) ahead of time.
Outline
• Monday: linear programming, dynamic programming, network flows
• Tuesday: optimal transport toolbox 1 (discrete, one-dimensional, semi-discrete cases)
• Wednesday: optimal transport toolbox 2 (continuous transport, convex analysis, entropic regularization)
• Thursday: static and dynamic multinomial choice
• Friday: statistical estimation of models of matching with transfers
Synopsis
SYNOPSIS
Part I: Tools
Day 1: linear programming (Monday)
Block 1. Basics of linear programming (morning 1st half)
• Theory: linear programming duality; complementary slackness; minimax formulation
• Coding: How to eat optimally? Dataset: Stigler’s original diet data (1945).
Block 2. Network flow problems (morning 2nd half)
• Theory: directed graphs and min-cost flow problem
• Coding: How to find the shortest path through a network? Dataset: Paris subway; New York City street network.
Block 3. Dynamic programming as linear programming (afternoon)
• Theory: Bellman’s equation; interpretation of duality; forward induction, backward induction
• Coding: When to repair mechanical engines? Dataset: Rust’s bus maintenance data (1994).
Day 2: optimal transport I (Tuesday)
Block 4. Discrete matching (morning 1st half)
• Theory: Shapley-Shubik duality; stability; decentralized equilibrium
• Coding: How to solve it? Dataset from Dupuy and Galichon (JPE 2014).
Block 5. Positive assortative matching (morning 2nd half)
• Theory: Becker’s model; compensating differentials; comonotonicity
• Coding: What is a CEO worth? Dataset: Gabaix-Landier’s (QJE 2008) CEO pay data.
Block 6. Hotelling’s characteristics model (afternoon)
• Theory: power diagrams, Aurenhammer’s method
• Coding: How to infer the unobservable quality of a car model? Dataset: Feenstra-Levinsohn (Restud 1994) car data.
Day 3: optimal transport II (Wednesday)
Block 7. Continuous multivariate matching (morning 1st half)
• Theory: Knott-Smith criterion; Brenier’s map; McCann’s theorem
• Applications: exercises.
Block 8. A short tutorial on convex analysis (morning 2nd half)
• Theory: convex duality; Fenchel’s inequality; subdifferentials and their inverses
• Application: exercises.
Block 9. Regularized optimal transport (afternoon)
• Theory: optimal transport with entropic regularization, and with other regularizations.
• Coding: coordinate descent and the IPFP algorithm.
Part II. Models
Day 4: models of static and dynamic multinomial choice (Thursday)
Block 10. Basics of static discrete choice (morning 1st half)
• Theory: Dary-Zachary-Williams theorem, generalized entropy of choice, the inversion theorem
• Coding: How to solve it? simulation methods; AR, SARS, and GHK. Dataset: Greene and Hensher (1997) data on choice of travel mode.
Block 11. Demand models, old and new (morning 2nd half)
• Theory: the GEV model; the random coefficient logit model and the pure characteristics models
• Coding: How to estimate demand for automobiles? Dataset: BLP.
Block 12. Dynamic discrete choice methods (afternoon)
• Theory: Rust’s model; estimation; normalization issues
• Coding: maintenance choice.
Day 5: empirical matching models, the quasilinear case (Friday)
Block 13. Separable models of matching (morning 1st half)
• Theory: matching with unobservable heterogeneity
• Coding: Did Roe vs. Wade decrease the value of marriage? Dataset: Choo and Siow (JPE 2006).
Block 14. The gravity equation (morning 2nd half)
• Theory: optimal transport and the gravity equation; generalized linear models and pseudo-Poisson maximum likelihood estimation
• Coding: How to forecast international trade flows? estimating the gravity equation based on WTO international trade data.
Block 15. High-dimensional matching models (afternoon)
• Theory: estimation of rank-constrained models
• Application: Does physical appearance have a price? matching on socioeconomic and anthropomorphic characteristics. Dataset: Chiappori, Oreffice and Quintana-Domeque’s (JPE 2012).
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.
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.”
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”.
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”.
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”.
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”.
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.
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.
May 20 2021, 1pm (public). Professor Guillaume Carlier (Paris-Dauphine University), on “the linear convergence of the multi-marginal Sinkhorn algorithm.”
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.
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.
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’
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.
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’
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’
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.
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:
This short course is focused on optimal transport theory and matching models and their applications to economics, in various fields such as labor markets, economics of marriage, industrial organization, matching platforms, networks, and international trade. It will provide the crossed perspectives of theory, empirics and computation. A particular emphasis will be given on computation (R and Python). This course is partly based on Galichon’s 2016 monograph, Optimal Transport Methods in Economics. Princeton University Press.
Schedule
Wednesday, June 24, 9am-12:30pm
Thursday, June 25, 9am-12:30pm
Friday, June 26, 9am-11am
Course material
The lecture slides will be available before each lecture.
References
These lectures will be based on my text:
Galichon, A. (2016). Optimal transport methods in economics. Princeton.
Other references include:
∙ For mathematical foundations:
– [OTON] C. Villani, Optimal Transport: Old and New, AMS, 2008.
– [OTAM] F. Santambrogio, Optimal Transport for Applied Mathematicians, Birkhäuser, 2015.
∙ For an introduction with a fluid mechanics point of view:
– [TOT] C. Villani, Topics in Optimal Transportation, AMS, 2003.
∙ With a computational focus:
– [NOT] G. Peyré, M. Cuturi (2018). Numerical optimal transport, Arxiv.
∙ With a family economics focus:
– [MWT] P.-A. Chiappori. Matching with Transfers: The Economics of Love and Marriage, Princeton, 2017.
Outline
• intro to optimal transport (3h)
• multinomial choice (3h)
• matching models (3h)
