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.

In the framework of bilateral assignment games, we study the set of matrices associated with assignment markets with the same core. We state conditions on matrix entries that ensure that the related assignment games have the same core. We prove that the set of matrices leading to the same core...

A matrix A defines an assignment market, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces aij units of utility. Quint (1991) points out that usually many different assignment matrices exist that define markets with the same core...