Technical note: Characterization of binomial semivalues through delegation games

Abstract

Semivalues are allocation rules for cooperative games that assign to each player in a given game a weighted sum of his marginal contributions to all coalitions he belongs to, where the weighting coefficients depend only on the coalition size. Binomial semivalues are a special class of semivalues whose weighting coefficients are obtained by means of a unique parameter. In particular, the Banzhaf value is a binomial semivalue. In this article, we provide an axiomatic characterization for each binomial semivalue.

The Prediction Value

“…It follows that semivalues which allow for the interpretation as a prediction value form a special subclass of semivalues. They are known as binomial semivalues (see Dubey et al 1981;Carreras and Freixas 2008; Puente 2012 -an axiomatic characterization has been given by Amer and Giménez 2007). Specifically, a p-binomial semivalue is defined by…”