Probabilistic Network Values

Marginality and the position value

“…The position value has received a lot of attention from game theorists. Algaba et al (2000) defined the position value for union stable systems, Casajus (2007) proved that the position value is, in some sense, the Myerson value, Gómez et al (2004) introduced a unified approach for the Myerson and the position values, Kongo (2010) established that the difference between the position value and the Myerson value is attributable to the existence of coalition structures, Ghintran et al (2012) extended it to the probabilistic communication situations, Ghintran (2010) defined a weighted position value, Xianghui et al (2017) defined the position value for communication situations with fuzzy coalitions, Fernández et al (2018) introduced the cg-position value for games on fuzzy communication structures, Zhang et al (2019) and Shan et al (2020) characterized the position value for hypergraph communications situations, and Borkotokey et al (2020) characterized it (and also the Myerson value) for the subclass of probabilistic network games in multilinear form.…”