Lexicographic allocations and extreme core payoffs: the case of assignment games

Characterization of the extreme core allocations of the assignment game

Two remarks on the inner core

For the case of smooth concave exchange economies, we provide a characterization of the inner core as the set of feasible allocations such that no coalition can improve on it, even if coalitions are allowed to use some random plans. For the case of compactly generated games, we discuss Myerson’s definition of the inner core, and we characterize it using lexicographic utility weight systems.  2...

A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...

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 maxpayoff vectors. Each one of these vectors is obtained recursively only making use of the assignment matrix. Those max-payoff vectors that are efficient turn up to give the extreme core allocations of the market. When the assignment market has large core (that is to s...

Cooperative assignment games with the inverse Monge property

We study inverse-Monge assignment games, namely cooperative assignment games in which the assignment matrix satisfies the inverse Monge property. For square inverse-Monge assignment games, we describe their cores and we obtain a closed formula for the buyers-optimal and the sellers-optimal core allocations. We also apply the above results to solve the non-square case.