Permutation games: another class of totally balanced games

Abstract

A class of cooperative games in characteristic function form arising from certain sequencing problems and assignment problems, is introduced. It is shown that games of this class are totally balanced. In the proof of this fact we use the Birkhoff-von Neumann theorem on doubly stochastic matrices and the Bondareva-Shapley theorem on balanced games. It turns out that this class of permutation games coincides with the class of totally balanced games if the number of players is smaller than four. For larger games the class of permutation games is a nonconvex subset of the convex cone of totally balanced games.