TraME  

TraME (Transportation Methods for Econometrics) is a C++ library for solving problems of equilibrium computation and estimation in consumer demand and matching frameworks via the Mass Transportation Approach.

Installation and Testing

TraME can be installed via

# clone TraME into the current directory
git clone https://github.com/TraME-Project/TraME ./trame
# build and install
cd ./trame
./configure -i "/usr/local" -p
make
make install

This will install TraME into /usr/local.

There are several configuration options available (./configure -h):

• -c a coverage build (used with Codecov)
• -d a 'development' build
• -g a debugging build (optimization flags set to -O0 -g)
• -h print help
• -i install path; default: current directory
• -l specify the linear programming library to link against, either GLPK (-l glpk) or Gurobi (-l gurobi)
• -m specify the BLAS and Lapack libraries to link against; for example, -m "-lopenblas" or -m "-framework Accelerate"
• -o compiler optimization options; defaults to -O3 -march=native -ffp-contract=fast
• -p enable OpenMP parallelization features

Example

The following example constructs several matching function-based markets under different matching technologies, then solves for equilibrium using the iterated proportional fitting procedure (IPFP) algorithm.

#include "trame.hpp"

int main()
{
    int nbX = 18;      // number of x types
    int nbY = 5;       // number of y types
    double sigma = 1;  // scaling value

    arma::vec n = arma::ones(nbX,1); // number of agents of each type
    arma::vec m = arma::ones(nbY,1);

    // systematic utilities

    arma::mat alpha  = arma::randu(nbX,nbY);
    arma::mat gamma  = arma::randu(nbX,nbY);
    arma::mat lambda = 1 + arma::randu(nbX,nbY);
    arma::mat zeta   = 1 + arma::randu(nbX,nbY);

    arma::mat phi = alpha + gamma;

    arma::mat lambda_LTU = lambda/(lambda+zeta);
    arma::mat phi_LTU = (lambda%alpha + zeta%gamma) / (lambda+zeta);

    // build markets

    trame::mfe<trame::mmfs::geo> mfe_obj_TU(sigma,false);
    mfe_obj_TU.build(n,m,phi); // geometric matching function <=> perfectly transferable utility

    trame::mfe<trame::mmfs::cd> mfe_obj_LTU(sigma,false);
    mfe_obj_LTU.build(n,m,lambda_LTU,phi_LTU); // CD matching function <=> linearly transferable utility

    trame::mfe<trame::mmfs::min> mfe_obj_NTU(sigma,false);
    mfe_obj_NTU.build(n,m,alpha,gamma); // min matching function <=> non-transferable utility

    //

    arma::mat mu_TU, mu_LTU, mu_NTU;

    mfe_obj_TU.solve(mu_TU);
    arma::cout << "Solution of TU-logit problem using ipfp:\n" << mu_TU << arma::endl;

    trame::ipfp(mfe_obj_LTU,mu_LTU);
    arma::cout << "Solution of LTU-logit problem using ipfp:\n" << mu_LTU << arma::endl;

    trame::ipfp(mfe_obj_NTU,mu_NTU);
    arma::cout << "Solution of NTU-logit problem using ipfp:\n" << mu_NTU << arma::endl;
}

Authors

Alfred Galichon and Keith O'Hara

License

GPL (>= 2)

Acknowledgements

Work on TraME is supported by NSF Grant DMS-1716489