Description Usage Arguments Value Author(s) References Examples
Finds the stable matching in the stable roommates problem with transferable utility. Uses the Partitioning Linear Programme formulated in Quint (1991).
1 |
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.
Valuation.matrix |
input values of V. |
Assignment.matrix |
upper triangular matrix of dimension |
Equilibrium.groups |
matrix that gives the |
Thilo Klein
Quint, T. (1991). Necessary and sufficient conditions for balancedness in partitioning games. Mathematical Social Sciences, 22(1):87–91.
1 2 3 4 5 6 |
$Valuation.matrix
1 2 3 4 5 6
1 -1.0511839 -0.2748335 1.7862302 0.46639025 0.17982907 1.37798683
2 -0.1407944 1.3560065 -1.1301338 1.26309033 0.54403042 0.86934000
3 -0.8391967 -2.5623605 -1.9935431 0.22183165 -0.18278726 0.51818310
4 0.1440278 -1.1413821 -0.5642685 -0.76359436 0.14679380 0.09327806
5 0.7588983 0.9038625 0.3482461 1.40449860 -0.81402126 0.65564475
6 0.1055536 0.3992842 -1.3420181 -3.00587123 0.08286898 0.24987036
7 1.1101963 1.1845576 0.3580491 -0.20497910 0.72142186 0.89366039
8 2.2027727 -0.1960047 2.3357905 0.07108017 -0.34701814 -0.93633273
9 1.2030322 -0.4446492 0.3281638 -1.38577616 -1.18155472 -0.21918175
10 -0.1053091 0.2450385 -1.7015642 -0.73070131 0.58816362 -1.28963489
7 8 9 10
1 1.396714653 0.6203378 0.771995369 0.17878748
2 0.325106450 1.2205936 1.211721580 -0.25449787
3 0.969324927 -2.1984178 -0.003559335 0.22836721
4 -0.577056639 -1.0763463 0.068304684 0.07334178
5 -0.004774385 0.2228761 1.443669078 -0.73854751
6 0.270165707 1.0826882 0.005452877 -0.03774491
7 -0.368620505 -0.4135712 -0.129601177 -0.21364931
8 1.353459362 -1.5304765 -0.500572000 0.97717939
9 -1.200715705 3.5964777 -0.807835545 1.13159648
10 -0.839302784 -0.7264529 0.582917492 -0.94209981
$Assignment.matrix
1 2 3 4 5 6 7 8 9 10
1 NA 0 0 0 0 0 0 1 0 0
2 NA NA 0 0 0 1 0 0 0 0
3 NA NA NA 0 0 0 1 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 0 0
9 NA NA NA NA NA NA NA NA NA 1
10 NA NA NA NA NA NA NA NA NA NA
$Equilibrium.groups
player.A player.B mutual.valuation
1 4 5 1.551292
2 2 6 1.268624
3 3 7 1.327374
4 1 8 2.823111
5 9 10 1.714514
$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
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