We give conditions to compute the extreme core allocations of a multisided assignment game. The way to compute the extreme core points rely on the extreme core points of a suitable finite family of cooperative games

We provide explicit formulas for the nucleolus of an arbitrary assignment game with two buyers and two sellers. Five different cases are analyzed depending on the entries of the assignment matrix. We extend the results to the case of 2 x m or m x 2 assignment games.