Given a game and two players, this function checks if those are symmetric players.
Usage
symmetrycheck(v, i, j, binary = FALSE, tol = 100 * .Machine$double.eps)
Value
TRUE if i and j are symmetric in v, FALSE otherwise.
Arguments
v
A characteristic function, as a vector.
i
The position of an individual coalition, as an integer.
j
The position of another individual coalition, as an integer.
binary
A logical value. By default, binary=FALSE. Should be set to TRUE if v, i and j are introduced in binary order instead of lexicographic order.
tol
A tolerance parameter, as a non-negative number.
By default, tol=100*.Machine$double.eps.
Details
Let \(v\in G^N\). Players \(i,j \in N\) are symmetric in \(v\) if,
for each \(S \subset N\) with \(i,j \in S\), \(v(S \setminus \{i\}) = v(S \setminus \{j\})\).