# mstGames: Cooperative games from minimum cost spanning tree problems In cooptrees: Cooperative aspects of optimal trees in weighted graphs

## Description

Given a graph with at least one minimum cost spanning tree, `mstGames` builds both cooperative games: the pessimistic and the optimistic game.

The pessimistic game associated with a minimum cost spanning tree problem is a cooperative game in which every coalition of agents obtains the minimum cost assuming that the agents outside the coalition are not connected.

The optimistic game associated with with a minimum cost spanning tree problem is a cooperative game in which every coalition of agents obtains the minimum cost assuming that that the agents outside the coalition are connected. Thus, the agents in the coalition can benefit from their connections to the source

## Usage

 `1` ```mstGames(nodes, arcs, game, show.data = TRUE) ```

## 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. `game` denotes the game that we want to obtain: "pessimistic" or "optimistic". `show.data` logical value indicating if the function displays the console output (`TRUE`) or not (`FALSE`). By default its value is `TRUE`.

## Value

`mstGames` returns a vector with the characteristic fuction of the selected game associated with the graph and prints the result in console.

## Examples

 ```1 2 3 4 5 6 7``` ```# 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) # Cooperative games mstGames(nodes, arcs, game = "pessimistic") mstGames(nodes, arcs, game = "optimistic") ```

### Example output

```Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

decompose, spectrum

The following object is masked from 'package:base':

union

v(S) =  6 10 6 10 12 10 14
\$coalitions
[1] "1"     "2"     "3"     "1,2"   "1,3"   "2,3"   "1,2,3"

\$values
[1]  6 10  6 10 12 10 14

v(S) =  4 4 4 8 8 8 14
\$coalitions
[1] "1"     "2"     "3"     "1,2"   "1,3"   "2,3"   "1,2,3"

\$values
[1]  4  4  4  8  8  8 14
```

cooptrees documentation built on May 30, 2017, 8:11 a.m.