A pairwise-monotonic core selection for permutation games

In this article, a single-valued solution for permutation games is proposed. If we consider that each agent on the permutation game acts both as a buyer and as a seller, a related assignment game with the same reward matrix is defined. In this two-sided related market, the midpoint between the buyers-optimal core allocation and the sellers-optimal core allocation is considered. Then, each agent in the permutation game merges his payoff as a buyer and his payoff as a seller. This solution belongs to the core of the one-sided market and it is pairwise-monotonic.