savingsgame {TUGLab}R Documentation

Savings game

Description

Given a cost game, this function returns the associated savings game.

Usage

savingsgame(c, binary = FALSE)

Arguments

c

The characteristic function of a cost game, as a vector.

binary

A logical value. By default, binary=FALSE. Should be set to TRUE if c is introduced in binary order instead of lexicographic order.

Details

Let c\in G^N be a cost game. Its associated savings game, v_c\in G^N, is defined by

v_{c}(S)=\sum_{i\in S}c(i)-c(S) \text{ for each }S\in 2^N.

Thus, for each coalition S, v_{c}(S) can be interpreted as the collective reduction of cost resulting from the cooperation of the members of S, with respect to the scenario of non-cooperation.

Value

The characteristic function of the savings game, as a vector in binary order if binary=TRUE and in lexicographic order otherwise.

See Also

airfieldgame, zeronormalizedgame

Examples

savingsgame(c(360,60,288,390,468,318,468))
v.random <- rnorm(2^5-1,58,13)
savingsgame(v.random) == -zeronormalizedgame(v.random)

[Package TUGLab version 0.0.1 Index]