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.
Document Type: | Working Paper |
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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): | ![]() |