`ttc.Rd`

Implements an algorithm for the house allocation problem proposed by Abdulkadiroglu and Sonmez (1999) for a matching problem in which there are both vacant houses and existing tenants.

ttc(nStudents = ncol(s.prefs), nHouses = length(houses), s.prefs, houses, priority = NULL, seed = NULL)

nStudents | integer indicating the number of students. Defaults to |
---|---|

nHouses | integer indicating the number of houses. Defaults to |

s.prefs | matrix of dimension |

houses | vector of length |

priority | (Optional) vector of length |

seed | (Optional) integer setting the state for random number generation. Defaults to seed = NULL |

`ttc`

returns a data frame of the matching of students (int) to houses (obj) for the house allocation problem based on the Top-Trading-Cycles algorithm.

Abdulkadiroglu, A. and T. Sonmez (1999). House Allocation with Existing Tenants. *Journal of Economic Theory*, 88 (2): 233-260.

Shapley, L. and H. Scarf (1974). On Cores and Indivisibility. *Journal of Mathematical Economics*, 1(1): 23-37.

##\dontrun{ ## 1-a. Generate matrix of individuals' preference rankings over objects, ## a.k.a. Rank Order Lists (ROL). s.prefs <- matrix(c(3,2,4,1, # ROL of student 1 3,5,6, NA, 3,1, NA,NA, 2,5,6,4, 1,3,2,NA, 2,4,5,6), nrow = 4, ncol = 6, byrow = FALSE); s.prefs#> [,1] [,2] [,3] [,4] [,5] [,6] #> [1,] 3 3 3 2 1 2 #> [2,] 2 5 1 5 3 4 #> [3,] 4 6 NA 6 2 5 #> [4,] 1 NA NA 4 NA 6## 1-b. Generate vector of house occupation objects ('obj') and their owners ('ind') (houses <- 1:6)#> [1] 1 2 3 4 5 6## 1-c. Find assignment based on TTC algorithm ttc(s.prefs = s.prefs, houses = houses, nHouses = 6, priority = 1:6)#> ind obj #> 1 1 2 #> 21 2 5 #> 2 3 3 #> 11 4 6 #> 3 5 1 #> 22 6 4## 2-a.Compare the example in the paper Abdulkadiroglu et al. (1999) ## on page 246-248 (section 5.1 An Example): ## generate matrix of students' preference rankings over houses, a.k.a. Rank Order Lists (ROL) s.prefs <- matrix(c(2,6,5,1,4,3,7,NA, 7,1,6,5,4,3,2,NA, 2,1,4,7,3,6,5,NA, 2,4,3,6,1,7,5,NA, 4,3,7,1,2,5,6,NA), byrow = FALSE, ncol= 5); s.prefs#> [,1] [,2] [,3] [,4] [,5] #> [1,] 2 7 2 2 4 #> [2,] 6 1 1 4 3 #> [3,] 5 6 4 3 7 #> [4,] 1 5 7 6 1 #> [5,] 4 4 3 1 2 #> [6,] 3 3 6 7 5 #> [7,] 7 2 5 5 6 #> [8,] NA NA NA NA NA## 2-b. Generate house occupation, so student 1 lives in house 1, ..., student 4 lives in house 4 ## and the other houses are vacant. houses <- c(1,2,3,4,NA,NA,NA,NA); houses#> [1] 1 2 3 4 NA NA NA NA## 2-c. Generate priority ordering priority <- 1:5 ## 2-d. Find assigment ttc(s.prefs = s.prefs, houses = houses, priority = priority)#> ind obj #> 1 1 2 #> 2 2 7 #> 3 3 1 #> 4 4 4 #> 5 5 3##}