36 research outputs found
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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 coalitional-games axioms for the Shapley value: efficiency, symmetry, and null player
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The Cooperative Solution of Stochastic Games
Building on the work of Nash, Harsanyi, and Shapley, we define a cooperative solution for strategic games that takes account of both the competitive and the cooperative aspects of such games. We prove
existence in the general (NTU) case and uniqueness in the TU case. Our main result is an extension of the definition and the existence and uniqueness theorems to stochastic games - discounted or undiscounted