# mstKar

0th

Percentile

##### Kar rule for minimum cost spanning tree problems

Given a graph with at least one minimum cost spanning tree, the mstKar function divides the cost of the tree among the agents according to the Kar rule. That rule is obtained with the Shapley value of the pessimistic game.

##### Usage
mstKar(nodes, arcs)
##### Arguments
nodes
vector containing the nodes of the graph, identified by a number that goes from $1$ to the order of the graph.
arcs
matrix with the list of arcs of the graph. Each row represents one arc. The first two columns contain the two endpoints of each arc and the third column contains their weights.
##### Value

mstKar returns a matrix with the agents and their costs.

The more general function mstRules.

• mstKar
##### Examples
# Graph
nodes <- 1:4
arcs <- matrix(c(1,2,6, 1,3,10, 1,4,6, 2,3,4, 2,4,6, 3,4,4),
byrow = TRUE, ncol = 3)
# Kar
mstKar(nodes, arcs)

Documentation reproduced from package cooptrees, version 1.0, License: GPL-3

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