Brown Bag Seminar: Ata Atay

We study transportation games that model many-to-many matching markets with transferable utility. This model has been considered by Sánchez-Soriano et al.(2001) and Sotomayor(2002). We investigate to which extent the known results on the assignment game (one-to-one matching markets with transferable utility) can be carried over to the transportation games. First, we show that, unlike the assignment game, transportation games are not INTO-lemaral. Sotomayor(2002) showed that there is no opposition of interest between the two sides of the market and the core is not a lattice. We conjecture that, for a given non-degenerate transportation game, there is (at least one) core vertex where all sellers get their core maximum payoffs; and there is (at least one) core vertex where all buyers get their core maximum payoffs. Secondly, we study the relationship between the set-wise solution concepts. We show that the kernel need not be a subset of the core of a transportation game, and hence the classical bargaining set and the core do not coincide. Finally, for transportation games, we see that single-valued solution the tau-value need not be a core allocation.