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Second-order productivity, second-order payoffs, and the Shapley value

  • 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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Document Type:Article
Author:André CasajusORCiD
Chairs and Professorships:Chair of Economics and Information Systems
Parent Title (English):Discrete applied mathematics
Issue:304 (December 2021)
Year of Completion:2021
First Page:212
Last Page:219
Tag:Second-order marginal contributions; Second-order marginality; Second-order symmetry; Shapley value; TU game
Content Focus:Academic Audience
Peer Reviewed:Yes
Rankings:AJG Ranking / 2
VHB Ranking / A
SJR Ranking / Q2
Licence (German):License LogoUrheberrechtlich geschützt