On the extreme points of the core of neighbour games and assignment games

Neighbour games arise from certain matching or sequencing situations in which only some specific pairs of players can obtain a positive gain. As a consequence, neighbour games are as well assignment games as line graph restricted games. We will show that the intersection of the class of assignment games and the class of line graph restricted games yields the class of neighbour games. Further, we give a necessary and sufficient condition for the convexity of neighbour games. In spite of the possible non-convexity of neighbour games, it turns out that for any neighbour game the extreme points of the core are marginal vectors. Moreover, we prove this for assignment games in general. Hence, for any assignment game the core is the convex hull of some marginal vectors.