Fractional solutions for NTU-games, with applications to stable matching problems
Peter Biro
Glasgow

(joint work with Tamas Fleiner)

abstract: In this talk I will survey some applications of the Scarf 
algorithm. First, I will introduce the notion of fractional core, which 
is always nonempty by the Scarf Lemma for finitely generated NTU-games. 
Stable allocation is a general solution concept for games where both the 
players and their possible cooperations may have capacities. Our main 
result is that, given a finitely generated NTU-game with capacities, we 
can always find a stable allocation by a variant of Scarf’s algorithm. I 
will explain the meaning of these results in the context of stable 
matching problems, and finally I will show some experiments for the 
Hospitals/Residents problem with couples.