Analysis of Stable Matchings in R

The `matchingMarkets`

R package 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 five 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).`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:

```
install.packages("matchingMarkets")
library(matchingMarkets)
```

Under Linux, the dependency package `gmp`

requires that you have GNU MP (> 4.1.4) installed, see http://gmplib.org.

To get the most recent *development version* from GitHub:

```
install.packages("devtools")
devtools::install_github("thiloklein/matchingMarkets")
library(matchingMarkets)
```

or from R-Forge:

```
install.packages("matchingMarkets", repos="http://R-Forge.R-project.org")
library(matchingMarkets)
```

Note: 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.

Package documentation is available at matchingMarkets.org and the vignette is available from the CRAN page. An application of the estimator in function `stabit`

is in Klein (2015).