Analysis of Stable Matchings in R

CRAN_Status_Badge CRAN_Downloads


matchingMarkets comes with two estimators:

  • stabit: Implements a Bayes estimator that corrects for sample selection in matching markets when the selection process is a one-sided matching game (i.e. group formation).

  • stabit2: Implements the Bayes estimator for a two-sided matching game (i.e. the college admissions and stable marriage problems).

and six algorithms that can be used to simulate matching data:

  • hri: Constraint model for the hospital/residents problem. Finds all stable matchings in two-sided matching markets. Implemented for both the stable marriage problem (one-to-one matching) and the hospital/residents problem, also known as college admissions problem (many-to-one matching).

  • hri2: Roth-Peranson Algorithm for the hospital/residents problem with couples. Finds the resident-optimal stable matching (if one exists) in the two-sided matching market.

  • iaa: Immediate Acceptance Algorithm (a.k.a. Boston mechanism): First-preference-first algorithm used for school choice in many countries. And Gale-Shapley Deferred Acceptance Algorithm.

  • sri: Constraint model for the stable roommates problem. Finds all stable matchings in the roommates problem (one-sided matching market).

  • plp: Partitioning Linear Programme. Finds stable matchings in the roommates problem (one-sided matching market) with transferable utility.

  • ttc: Top-Trading-Cycles Algorithm. Finds stable matchings in the housing market problem.

Functions hri and sri are based on Patrick Prosser's n-ary constraint encoding model. They allow for incomplete preference lists (some agents find certain agents unacceptable) and unbalanced instances (unequal number of agents on both sides).


Get started by installing the R software for statistical computing.

To get the latest stable version of the package from CRAN:


Under Linux, the dependency package gmp requires that you have GNU MP (> 4.1.4) installed: $ sudo apt-get install libgmp-dev. See

To get the most recent development version from GitHub:


or from R-Forge:

install.packages("matchingMarkets", repos="")

Java Note 1: If you get a Java error such as JAVA_HOME cannot be determined from the Registry, this can be resolved by installing a Java version (i.e. 64-bit Java or 32-bit Java) that fits to the type of R version that you are using (i.e. 64-bit R or 32-bit R). This problem can easily effect Windows 7 users, since they might have installed a version of Java that is different than the version of R they are using. See this post and download the Java version from the Oracle website.

Java Note 2: If the installation of the dependent rJava package fails with configuration failed for package rJava, this can be fixed in Linux by $ sudo apt-get install r-cran-rjava.


Package documentation is available at and the vignette is available from the CRAN page. An application of the estimator in function stabit is in Klein (2015).

Function reference


Gives an overview of the various functions used in the matchingMarkets package.


Documentation for the most common matching algorithms.

  • hri
    All stable matchings in the hospital/residents problem with incomplete lists
  • hri2
    Resident-optimal stable matching in the hospital/residents problem with couples and incomplete lists
  • iaa
    Immediate Acceptance Algorithm (a.k.a. Boston mechanism) for two-sided matching markets
  • sri
    All stable matchings in the stable roommates problem with incomplete lists
  • plp
    Partitioning Linear Programme for the stable roommates problem
  • ttc
    Top-Trading-Cycles Algorithm for the house allocation problem


Two structural estimators for one-sided and two-sided matching markets.

  • stabit(stabitSel2)
    Matching model and selection correction for group formation
  • stabit2(stabit2Mat1, stabit2Sel1, stabit2Sel2)
    Matching model and selection correction for college admissions

Data generation

Two functions to produce simulated data for one-sided and two-sided matching markets.

  • stabsim
    Simulated data for group formation problem
  • stabsim2
    Simulated data for college admissions problem


Description of three datasets for matching markets contained in the package.

  • baac00
    Townsend Thai Project BAAC Annual Resurvey, 2000
  • klein15a
    MCMC results in Klein (2015a)
  • klein15b
    Results of Monte Carlo Simulations in Klein (2015b)


  • khb
    Karlson-Holm-Breen method for comparing probit coefficients
  • mce
    MC Experiments