Cooperative Strategic Games

We examine a solution concept, called the “value,” for n-person strategic games. In applications, the value provides an a-priori assessment of the monetary worth of a player’s position in a strategic game, comprising not only the player’s contribution to the total payoff but also the player’s ability to inflict losses on other players. A salient feature is that the value takes account of the costs that “spoilers” impose on themselves. Our main result is an axiomatic characterization of the value. For every subset, S, consider the zero-sum game played between S and its complement, where the players in each of these sets collaborate as a single player, and where the payoff is the difference between the sum of the payoffs to the players in S and the sum of payoffs to the players not in S. We say that S has an effective threat if the minmax value of this game is positive. The first axiom is that if no subset of players has an effective threat then all players are allocated the same amount. The second axiom is that if the overall payoff to the players in a game is the sum of their payoffs in two unrelated games then the overall value is the sum of the values in these two games. The remaining axioms are the strategic-game analogs of the classical coalitionalgames axioms for the Shapley value: efficiency, symmetry, and null player. Keyword: Strategic games, cooperative games, Nash bargaining, Shapley value, threats, bribes, corruption. ∗Harvard Business School, Harvard University; [email protected]. †Institute of Mathematics, and the Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel; [email protected]. The research of A. Neyman was supported in part by Israel Science Foundation grant 1596/10.