Abstract:

A game of threats on a finite set of players, $N$, is a function $d$ that assigns a real number to any coalition, $S subseteq N$, such that $d left( S right) = - d left( N setminus S right)$. A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition $d left( emptyset right) = 0$. We show that analogs of the classic Shapley axioms for coaltional games determine a unique value for games of threats. This value assigns to each player an average of the threat powers, $d left( S right)$, of the coalitions that include the player.

Website