Fairness and fairness for neighbors: The difference between the Myerson value and component-wise egalitarian solutions

We replace the axiom of fairness used in the characterization of the Myerson value (Myerson, 1977) by fairness for neighbors in order to characterize the component-wise egalitarian solution. When a link is broken, fairness states that the two players incident to the link should be affected similarly while fairness for neighbors states that a player incident to the link and any of his other neighbors should be affected similarly. Fairness for neighbors is also used to characterize the component-wise egalitarian surplus solution and a two-step egalitarian surplus solution. These results highlight that egalitarian and marginalistic allocation rules can be obtained by applying the same equal gain/loss property to different types of players.

► We replace the axiom of fairness (Myerson, 1977) by fairness for neighbors. ► A player incident to a broken link and his other neighbors are affected similarly. ► We characterize three types of component-wise egalitarian solutions. ► Egalitarian and marginalistic rules results from similar equal gain/loss properties.