Description

This script implement in JAX a fixed point iteration algorithm to solve a class of one-to-one matching model with linear transfers.

The main script is SolveOneToOneMatching.py that sets up and solves a general system of fixed point equations for the set of equilibrium transfers in a one-to-one matching model. The script run_test.py uses the main script to solve three special cases of one-to-one matching models, where the discrete choices of the agents on both sides of the matching market are described by the

• Logit model
• Nested logit model
• Generalized nested logit model

Citations

If you use this script in your research, I ask that you also cite Andersen (2024).

@article{andersen2024notesolvingonetoonematching,
  title={Note on solving one-to-one matching models with linear transferable utility}, 
  author={Esben Scrivers Andersen},
  year={2024},
  eprint={2409.05518},
  archivePrefix={arXiv},
  primaryClass={econ.GN},
  url={https://arxiv.org/abs/2409.05518}, 
}

Installation

In order to run the scripts, you need to have installed JAX, Simple Pytree, and FixedPointJAX. The latter is an implementation of a fixed point iteration algorithm that allow the user to solve the system of fixed point equations by standard fixed point iterations and the SQUAREM accelerator, see Du and Varadhan (2020).

You can install the current release of FixedPointJAX with pip

pip install FixedPointJAX

You can install the current release of JAX with pip

pip install jax

You can install the current release of Simple Pytree with pip

pip install simple-pytree