# Alternative representation of semivalues, the inverse problem and coalitional rationality

Working paper

Issue number:

2019/10

Series:

CORE Discussion Papers

Publisher:

CORE - Université Catholique de Louvain

Year:

2019

The concept of semivalue of a transferable utility game has been introduced by Dubey, Neyman
and Weber as weighted sum of marginal contributions. Later, Puente has introduced a particular
class of semivalues, called binomial semivalues, where weights are obtained through a recursive
procedure. In the present paper, we extend Puente's procedure to obtain an equivalent
representation of semivalues that turns out to be useful to solve the inverse problem and the
question of coalitional rationality.