matchingMarkets (version 0.1-1)

plp: Partitioning Linear Programme for the stable roommates problem

Description

Finds the stable matching in the http://en.wikipedia.org/wiki/Stable_roommates_problem{stable roommates problem} with transferable utility. Uses the Partitioning Linear Programme formulated in Quint (1991).

Usage

plp(V = NULL, N = NULL)

Arguments

N

integer (divisible by 2) that gives the number of players in the market.

V

valuation matrix of dimension NxN that gives row-players valuation over column players (or vice versa).

Value

• 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.

References

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

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)