Given a cost game, this function returns the associated savings game.
Usage
savingsgame(c, binary = FALSE)
Value
The characteristic function of the savings game, as a vector in binary order if binary=TRUE and in lexicographic order otherwise.
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.