A simple procedure to obtain the extreme core allocations of an assignment market

Given an assignment market, we introduce a set of vectors, one for each possible ordering on the player set, which we name the max-payoff vectors. Each one of these vectors is obtained recursively only making use of the assignment matrix. Those max-payoff vectors that are efficient turn out to give the extreme core allocations of the market. When the assignment game has a large core, all the max-payoff vectors are extreme core allocations.