Simple Combinatorial Optimisation Cost Games

Abstract

In this paper we introduce the class of simple combinatorial optimisation cost games, which are games associated to {0, 1}-matrices.A coalitional value of a combinatorial optimisation game is determined by solving an integer program associated with this matrix and the characteristic vector of the coalition.For this class of games, we will characterise core stability and totally balancedness.We continue by characterising exactness and largeness.Finally, we conclude the paper by applying our main results to minimum colouring games and minimum vertex cover games.Combinatorial optimisation game;core stability;totally balancedness;largeness;exactness