Abstract
We introduce the concepts of the players’ second-order productivities in cooperative games with transferable utility (TU games) and of the players’ second-order payoffs for one-point solutions for TU games. Second-order productivities are conceptualized as second-order marginal contributions, that is, how one player affects another player’s marginal contributions to coalitions containing neither of them by entering these coalitions. Second-order payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. We show that the Shapley value is the unique efficient one-point solution for TU games that reflects the players’ second-order productivities in terms of their second-order payoffs.
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