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, |
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)