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

André Casajus () and Rodrigue Tido Takeng ()
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André Casajus: HHL Leipzig Graduate School of Management
Rodrigue Tido Takeng: Normandie University

Annals of Operations Research, 2023, vol. 320, issue 1, No 1, 13 pages

Abstract: Abstract We introduce the concepts of the components’ second-order productivities in cooperative games with transferable utility (TU games) with a coalition structure (CS games) and of the components’ second-order payoffs for one-point solutions for CS games as generalizations of the players’ second-order productivities in TU games and of the players’ second-order payoffs for one-point solutions for TU games (Casajus in Discrete Appl Math 304:212–219, 2021). The players’ 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. The players’ second-order payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. Analogously, the components’ second-order productivities are conceptualized as their second-order productivities in the game between components; the components’ second-order payoffs are conceptualized as their second-order payoffs in the game between components. We show that the Owen value is the unique efficient one-point solution for CS games that reflects the players’ and the components’ second-order productivities in terms of their second-order payoffs.

Keywords: TU game; Shapley value; Owen value; Second-order marginal contributions; Second-order payoffs; 91A12; C71; D60 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10479-022-04974-z

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