Polar forms, \(p\)-values, and the core (Q2759587)

The author considers some new classes of infinite cooperative games of bounded polynomial variation and studies the Shapley value and the core. Based on a lattice theoretic approach the notions of polynomial and homogeneous polynomial games are introduced. The concept of polar form of homogeneous games are proposed and it is shown that there exists a unique polar form for any homogeneous polynomial game. One of the main results of the paper is a representation theorem that establishes a close relation between the Shapley value and the polar form of a homogeneous polynomial game. The author also presents some non-symmetric generalizations of the Shapley value and polar form.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00036].