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Disjointly productive players and the Shapley value

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

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Abstract

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, is removed from 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 in a game with the merged player does not change. These two axioms, along with efficiency, characterize the Shapley value and can lead to improved run times for computing the Shapley value in games with some disjointly productive players.

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