A classic example in coalitional game theory is the three-person majority game, in which the allocation of

Question:

A classic example in coalitional game theory is the three-person majority game, in which the allocation of $1 among three persons is decided by majority vote. Let N = {1, 2, 3}. The characteristic function is
w({i}) = 0, i = 1, 2, 3
w({i, j}) = 1, i, j ∈ N, i ≠ j
w(N) = 1
1. Show that the three-person majority game is cohesive.
2. Show that its core is empty.