codebin2lex: Binary order position to lexicographic order position
Description
Given the binary order position of a coalition, this function returns the corresponding lexicographic order position.
Usage
codebin2lex(n, Nbin)
Value
The corresponding lexicographic order position, as an integer between 1 and \(2^{\code{n}}-1\).
Arguments
n
Number of players, as an integer.
Nbin
A binary order position, as an integer between 1 and \(2^{\code{n}}-1\).
Details
The binary order position of a coalition \(S\in 2^N\) is given by \(\sum_{i\in S} 2^{i-1}\). Lexicographic order arranges coalitions in ascending order according to size, and applies lexicographic order to break ties among coalitions of the same size.