We extend Rochfords (1983) notion of symmetrically pairwise-bargained equilibrium to assignment games with more than two sides. A symmetrically multilateral-bargained (SMB) allocation is a core allocation such that any agent is in equilibrium with respect to a negotiation process among all...

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of...

We introduce the class of multi-sided B ohm-Bawerk assignment games, which generalizes the well-kown two-sided B ohm-Bawerk assignment games to situations with an arbitrary number of sectors. We reach the extreme core allocations of any multi-sided B ohm- Bawerk assignment game by means of an...

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with nonnegative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of...

I prove that, in assignment markets with more than two sides, agents of different sides (or sectors) need not be complements, whereas agents of the same side need not be substitutes. Shapley (1962) showed that this cannot happen when assignment markets are bilateral. Nevertheless, I found...

In the framework of two-sided assignment markets, we first consider that among several markets, the players may choose where to trade. It is shown that the corresponding game, represented by the maximum of a finite set of assignment games, may not be balanced. Some conditions for balancedness...

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the...

Singlevalued solutions for the case of twosided market games without product differentiation, also known as B ohmBawerk horse market games, are analyzed. The nucleolus is proved to coincide with the value, and is thus the midpoint of the core. Moreover a characterization of this set of games in...