A decomposition of the space of TU-games using addition and transfer invariance

Abstract

a b s t r a c tIn Béal et al. (forthcoming) two new axioms of invariance, called Addition invariance and Transfer invariance respectively, are introduced to design allocation rules for TU-games. Here, we derive direct-sum decompositions of the linear space of TU-games by using the TU-games selected to construct the operations of Addition and Transfer. These decompositions allow us to recover previous characterization results obtained by Béal et al. (forthcoming), to provide new characterizations of well-known (class of) allocation rules and also to design new allocation rules.

Characterization of the Average Tree solution and its kernel

“…Though this approach has been recently applied to classical TU-games -see, for instance, Béal et al (2013) and Yokote, (2014) -it has not been yet deeper investigated in the field of graph TU-games.…”

“…At last, another advantage of our method is that it proves very useful to show logical independence of the axioms used in the characterizations. Although this approach has already been undertaken for cooperative games with no restriction on the cooperation possibilities -see, for instance, Kleinberg and Weiss (1985), and more recently, Béal et al, (2013) and Yokote (2014) -, to the best of our knowledge, this is the first time it is applied to graph games.…”