Weakly differentially monotonic solutions for cooperative games
| Autor: | André Casajus, Koji Yokote |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Computer Science::Computer Science and Game Theory Economics and Econometrics Property (philosophy) Stochastic game Null (mathematics) Monotonic function Characterization (mathematics) Shapley value Mathematics (miscellaneous) Statistics Probability and Uncertainty Differential (infinitesimal) Mathematical economics Value (mathematics) Social Sciences (miscellaneous) Mathematics |
| Zdroj: | International Journal of Game Theory. 48:979-997 |
| ISSN: | 1432-1270 0020-7276 |
| DOI: | 10.1007/s00182-019-00669-1 |
| Popis: | The principle of differential monotonicity for cooperative games states that the differential of two players’ payoffs weakly increases whenever the differential of these players’ marginal contributions to coalitions containing neither of them weakly increases. Together with the standard efficiency property and a relaxation of the null player property, differential monotonicity characterizes the egalitarian Shapley values, i.e., the convex mixtures of the Shapley value and the equal division value for games with more than two players. For games that contain more than three players, we show that, cum grano salis, this characterization can be improved by using a substantially weaker property than differential monotonicity. Weak differential monotonicity refers to two players in situations where one player’s change of marginal contributions to coalitions containing neither of them is weakly greater than the other player’s change of these marginal contributions. If, in such situations, the latter player’s payoff weakly/strictly increases, then the former player’s payoff also weakly/strictly increases. |
| Databáze: | OpenAIRE |
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