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

  • 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, 2021, Discrete Appl. Math. 304, 212-219). 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.

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Metadaten
Document Type:Working Paper
Language:English
Author:André Casajus, Rodrigue Tido Takeng
Chairs and Professorships:Chair of Economics and Information Systems
Full text/ URN:urn:nbn:de:101:1-2021122013374563800066
Parent Title (English):HHL Working paper
ISSN:1864-4562
Series (Serial Number):HHL-Arbeitspapier / HHL Working paper (192)
Place of publication:Leipzig
Publisher:HHL Leipzig Graduate School of Management
Year of Completion:2021
Page Number:14
Tag:Owen value; Second-order marginal contributions; Second-order payo§s; Shapley value; TU Game
Licence (German):License LogoUrheberrechtlich geschützt