`iaa.Rd`

Finds the optimal assignment of students to colleges in the
college admissions problem
based on the Boston mechanism. The algorithmen is also applicable to the stable marriage problem. The option `acceptance="deferred"`

instead uses the Gale-Shapley
(1962) Deferred Acceptance Algorithm with student offer. The function works with either
given or randomly generated preferences.

iaa(nStudents = ncol(s.prefs), nColleges = ncol(c.prefs), nSlots = rep(1, nColleges), s.prefs = NULL, c.prefs = NULL, acceptance = "immediate", short_match = TRUE, seed = 123)

nStudents | integer indicating the number of students (in the college admissions problem)
or men (in the stable marriage problem) in the market. Defaults to |
---|---|

nColleges | integer indicating the number of colleges (in the college admissions problem)
or women (in the stable marriage problem) in the market. Defaults to |

nSlots | vector of length |

s.prefs | matrix of dimension |

c.prefs | matrix of dimension |

acceptance | if |

short_match | (Optional) If |

seed | (Optional) integer setting the state for random number generation. |

`iaa`

returns a list with the following elements.

student-side preference matrix.

college-side preference matrix.

number of interations required to find the stable matching.

edgelist of matches

identifier of single (or unmatched) students/men.

`iaa`

requires the following combination of arguments, subject to the matching problem.

`nStudents, nColleges`

Marriage problem with random preferences.

`s.prefs, c.prefs`

Marriage problem with given preferences.

`nStudents, nSlots`

College admissions problem with random preferences.

`s.prefs, c.prefs, nSlots`

College admissions problem with given preferences.

Gale, D. and Shapley, L.S. (1962). College admissions and the stability
of marriage. *The American Mathematical Monthly*, 69(1):9--15.

Kojima, F. and M.U. Unver (2014). The "Boston" school-choice mechanism. *Economic Theory*, 55(3): 515--544.

# NOT RUN { ## -------------------------------- ## --- College admission problem s.prefs <- matrix(c(1,2,3, 1,2,3, 1,2,3, 2,1,3, 2,1,3), byrow = FALSE, ncol = 5, nrow = 3); s.prefs c.prefs <- matrix(c(1,4,2,3,5, 5,2,3,4,1, 1,2,3,4,5), byrow = FALSE, ncol = 3, nrow = 5); c.prefs nSlots <- c(2,2,1) ## Boston mechanism iaa(s.prefs = s.prefs, c.prefs = c.prefs, nSlots = nSlots)$matchings ## Gale-Shapley algorithm iaa(s.prefs = s.prefs, c.prefs = c.prefs, nSlots = nSlots, acceptance="deferred")$matchings ## Same results for the Gale-Shapley algorithm with hri2() function (but different format) set.seed(123) iaa(nStudents=7, nSlots=c(3,3), acceptance="deferred")$matchings set.seed(123) hri2(nStudents=7, nSlots=c(3,3))$matchings # }