plp.RdFinds the stable matching in the stable roommates problem with transferable utility. Uses the Partitioning Linear Programme formulated in Quint (1991).
plp(V = NULL, N = NULL)
| V | valuation matrix of dimension |
|---|---|
| N | integer (divisible by 2) that gives the number of players in the market. |
plp returns a list with the following items.
input values of V.
upper triangular matrix of dimension NxN with entries of 1 for equilibrium pairs and 0 otherwise.
matrix that gives the N/2 equilibrium pairs and equilibrium partners' mutual valuations.
Quint, T. (1991). Necessary and sufficient conditions for balancedness in partitioning games. Mathematical Social Sciences, 22(1):87--91.
## Roommate problem with 10 players, transferable utility and random preferences: plp(N=10)#> $Valuation.matrix #> 1 2 3 4 5 6 #> 1 -0.5558411 -0.6250393 0.82158108 1.20796200 -0.2257710 -1.07179123 #> 2 1.7869131 -1.6866933 0.68864025 -1.12310858 1.5164706 0.30352864 #> 3 0.4978505 0.8377870 0.55391765 -0.40288484 -1.5487528 0.44820978 #> 4 -1.9666172 0.1533731 -0.06191171 -0.46665535 0.5846137 0.05300423 #> 5 0.7013559 -1.1381369 -0.30596266 0.77996512 0.1238542 0.92226747 #> 6 -0.4727914 1.2538149 -0.38047100 -0.08336907 0.2159416 2.05008469 #> 7 -1.0678237 0.4264642 -0.69470698 0.25331851 0.3796395 -0.49103117 #> 8 -0.2179749 -0.2950715 -0.20791728 -0.02854676 -0.5023235 -2.30916888 #> 9 -1.0260044 0.8951257 -1.26539635 -0.04287046 -0.3332074 1.00573852 #> 10 -0.7288912 0.8781335 2.16895597 1.36860228 -1.0185754 -0.70920076 #> 7 8 9 10 #> 1 -0.688008616 -0.2204866 1.3606524 -0.95161857 #> 2 1.025571370 0.3317820 -0.6002596 -0.04502772 #> 3 -0.284773007 1.0968390 2.1873330 -0.78490447 #> 4 -1.220717712 0.4351815 1.5326106 -1.66794194 #> 5 0.181303480 -0.3259316 -0.2357004 -0.38022652 #> 6 -0.138891362 1.1488076 -1.0264209 0.91899661 #> 7 0.005764186 0.9935039 -0.7104066 -0.57534696 #> 8 0.385280401 0.5483970 0.2568837 0.60796432 #> 9 -0.370660032 0.2387317 -0.2466919 -1.61788271 #> 10 0.644376549 -0.6279061 -0.3475426 -0.05556197 #> #> $Assignment.matrix #> 1 2 3 4 5 6 7 8 9 10 #> 1 NA 1 0 0 0 0 0 0 0 0 #> 2 NA NA 0 0 0 0 0 0 0 0 #> 3 NA NA NA 0 0 0 0 0 0 1 #> 4 NA NA NA NA 0 0 0 0 1 0 #> 5 NA NA NA NA NA 1 0 0 0 0 #> 6 NA NA NA NA NA NA 0 0 0 0 #> 7 NA NA NA NA NA NA NA 1 0 0 #> 8 NA NA NA NA NA NA NA NA 0 0 #> 9 NA NA NA NA NA NA NA NA NA 0 #> 10 NA NA NA NA NA NA NA NA NA NA #> #> $Equilibrium.groups #> player.A player.B mutual.valuation #> 1 1 2 1.161874 #> 2 5 6 1.138209 #> 3 7 8 1.378784 #> 4 4 9 1.489740 #> 5 3 10 1.384051 #>## Roommate problem with 10 players, transferable utility and given preferences: V <- matrix(rep(1:10, 10), 10, 10) plp(V=V)#> $Valuation.matrix #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] #> [1,] 1 1 1 1 1 1 1 1 1 1 #> [2,] 2 2 2 2 2 2 2 2 2 2 #> [3,] 3 3 3 3 3 3 3 3 3 3 #> [4,] 4 4 4 4 4 4 4 4 4 4 #> [5,] 5 5 5 5 5 5 5 5 5 5 #> [6,] 6 6 6 6 6 6 6 6 6 6 #> [7,] 7 7 7 7 7 7 7 7 7 7 #> [8,] 8 8 8 8 8 8 8 8 8 8 #> [9,] 9 9 9 9 9 9 9 9 9 9 #> [10,] 10 10 10 10 10 10 10 10 10 10 #> #> $Assignment.matrix #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] #> [1,] NA 0 0 0 0 0 0 0 0 1 #> [2,] NA NA 0 0 0 0 1 0 0 0 #> [3,] NA NA NA 0 0 1 0 0 0 0 #> [4,] NA NA NA NA 1 0 0 0 0 0 #> [5,] NA NA NA NA NA 0 0 0 0 0 #> [6,] NA NA NA NA NA NA 0 0 0 0 #> [7,] NA NA NA NA NA NA NA 0 0 0 #> [8,] NA NA NA NA NA NA NA NA 1 0 #> [9,] NA NA NA NA NA NA NA NA NA 0 #> [10,] NA NA NA NA NA NA NA NA NA NA #> #> $Equilibrium.groups #> player.A player.B mutual.valuation #> 1 4 5 9 #> 2 3 6 9 #> 3 2 7 9 #> 4 8 9 17 #> 5 1 10 11 #>