# equiprice

# EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing

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

*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. 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).

This project is hosted by Sciences Po.

## Seasonal events

### Summer: Alfred’s ‘math+econ+code’ masterclass

Summer 2020: masterclass on equilibrium transport and matching models in economics.

Summer 2021: masterclass on linear programming in economics.

Summer 2022: masterclass on optimal transport methods in economics.

Summer 2023: masterclass on network economics: trade, social networks, causality.

Summer 2024: masterclass on algorithms for economics.

### Fall: multidisciplinary retreat on open investigations

Fall 2020: Lattices, discrete convexity, and supermodularity

Fall 2021: Parallel computing

Fall 2022: Handling of large datasets

Fall 2023: Variational inequalities

Fall 2024: Lemke-Howson and Scarf lemma

### Winter: guest lecture series

Winter 2021 (a): General equilibrium with gross substitutes

Winter 2021 (b): Nonlinear complementarity problems

Winter 2022 (a): New trends in empirical industrial organization

Winter 2022 (b): Generated prescribed Jacobian equations

Winter 2023 (a): Discrete convexity, polymatroids and submodularity

Winter 2023 (b): Recent developments in optimal transport

Winter 2024 (a): Minimax-regret estimation

Winter 2024 (b): Scarf’s algorithm and its posterity

Winter 2025 (a): Schrodinger-Bernstein systems

Winter 2025 (b): Asynchronous Parallel Computing

### Spring: Paris research workshop

Spring 2021: Advances in computational economics.

Spring 2022: Universal gravity.

Spring 2023: Inference in models of matching with and without transferable utility.

Spring 2024: Optimal and equilibrium transport.

Spring 2025: Structural models of the labor market: inference, computation and model selection.

## SOFTWARE

### Project TraMEpy

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.

## Open positions

### OPEN: One 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.

### OPEN: Two doctoral fellows (TBA)

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

### OPEN: research interns (TBA)

Research intern positions are project-specific and will be announced later.

## Econ-coding challenge

To be announced lated.