Extensions of Hart and Mas-Colell’s Consistency to Efficient, Linear, and Symmetric Values for TU-Games

Modeling values for TU-games using generalized versions of consistency, standardness and the null player property

“…This new value (not studied in the literature yet) is different from the per-capita Shapley value introduced in Example 3 in Driessen and Radzik (2003).…”

“…An equivalent form of this generalization of the Shapley value was first introduced in Joosten et al (1994), and next axiomatized (in terms of consistency) by Joosten (1996, Chapter 5). The name "δ-discounted Shapley value" comes from Driessen and Radzik (2003).…”

“…In Driessen and Radzik (2003) we generalized their approach, considering generalized forms for both of these properties. The main results obtained there are completed in this section (Proposition 5 and Theorem 2) to "if and only if" forms.…”

“…They come from Driessen and Radzik (2003). The first one is related to some kind of generalized standardness for two-person games, and the second one describes some general notion of consistency which extends the reduced game property introduced by Hart and MasColell (1989).…”

“…Hart and Mas-Colell construct an elegant theory of potential for cooperative games and apply it to get an axiomatization of the Shapley value with the consistency axiom. Their theory is extended in Driessen and Radzik (2003) where the authors give an axiomatization based on generalized consistency properties for some wide class of values of cooperative games. The main results given there have been completed and remarkably strengthened in Sect.…”