Fractional solutions for NTU-games, with applications to stable matching problems
Dr Peter Biro
Institute of Economics, Hungarian Academy of Sciences
Introduced by Dr Daniel Paulusma
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.
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