Games of Threats

by Elon Kohlberg and Abraham Neyman

Overview — The Shapley value is the most widely studied solution concept of cooperative game theory, with applications to cost allocation, fair division, voting, etc. It is defined on coalitional games, which are the standards objects of the theory. The authors extend the Shapley value solution beyond coalitional games to “games of threats,” which arise in applications that combine competitive and cooperative considerations.

Author 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 ⊆ N, such that d(S) = -d(N\S). A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition d(Ø) = 0. We show that analogs of the classic Shapley axioms for coalitional games determine a unique value for games of threats. This value assigns to each player an average of the threat powers, d(S), of the coalitions that include the player.

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