perfectcoregame: Perfect core game
Description
This function returns the perfect core game with a given number of players.
Usage
perfectcoregame(n, binary = FALSE)
Value
The characteristic function of the perfect core game with n players, as a vector in binary order if binary=TRUE and in lexicographic order otherwise.
Arguments
- n
A number of players, as an integer.
- binary
A logical value. By default, binary=FALSE.
Details
The perfect core game of \(n\) players is defined by $$v_P(S)=s-\sqrt{\frac{s(n-s)}{n-1}}\text{ for all }S\in 2^N,$$ where \(s=|S|\).
References
Shapley, L. S. (1971). Cores of convex games. International Journal of Game Theory, 1(3), 11-26.