Games of Threats

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.