# mstKar

From cooptrees v1.0
by Manuel Fontenla

##### 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.
##### See Also

The more general function mstRules.

##### 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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