plp function

Partitioning Linear Programme for the stable roommates problem

Finds 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)

Arguments

• V: valuation matrix of dimension NxN that gives row-players valuation over column players (or vice versa).
• N: integer (divisible by 2) that gives the number of players in the market.

Returns

plp returns a list with the following items. - Valuation.matrix: input values of V.

• Assignment.matrix: upper triangular matrix of dimension NxN with entries of 1 for equilibrium pairs and 0 otherwise.

• Equilibrium.groups: matrix that gives the N/2 equilibrium pairs and equilibrium partners' mutual valuations.

Examples

## Roommate problem with 10 players, transferable utility and random preferences:
plp(N=10)

## Roommate problem with 10 players, transferable utility and given preferences:
V <- matrix(rep(1:10, 10), 10, 10)
plp(V=V)

References

Quint, T. (1991). Necessary and sufficient conditions for balancedness in partitioning games. Mathematical Social Sciences, 22(1):87--91.

Author(s)

Thilo Klein