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Disjointly and jointly productive players and the Shapley value

Besner, Manfred (2021): Disjointly and jointly productive players and the Shapley value.

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Central to this study is the concept of disjointly productive players. Two players are disjointly productive if there is no synergy effect if one of these players joins a coalition containing the other. Our first new axiom states that the payoff to a player does not change when another player, disjointly productive with that player, leaves the game. The second new axiom means that if we merge two disjointly productive players into a new player, the payoff to a third player does not change. These two axioms, along with efficiency, characterize the Shapley value and may be useful in improving the run time for computing the Shapley value in games with some disjointly productive players. Further axiomatizations of the Shapley value are provided in which jointly productive players, known as mutually dependent players, also play a role. Using a change of behavior property, the payoff for two players in two games in which their behavior changed once to total dislike and once to total like is equal to the payoff in the original game. Another axiomatization uses an additivity property for games in which two players have also changed their behavior to total non-cooperation.

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