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.
| Document Type: | Article |
|---|---|
| Language: | English |
| Author: | André Casajus |
| Chairs and Professorships: | Chair of Economics and Information Systems |
| DOI: | https://doi.org/10.1016/j.dam.2021.07.036 |
| Parent Title (English): | Discrete applied mathematics |
| ISSN: | 0166-218X |
| 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): |  Urheberrechtlich geschützt |