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2386. On the Owen core of many-to-one assignment games

Invited abstract in session MA-36: Game Theory, Solutions and Structures I, stream Game Theory, Solutions and Structures.

Monday, 8:30-10:00
Room: 32 (building: 306)

Authors (first author is the speaker)

1. Tamás Solymosi
Operations Research and Actuarial Sciences, Corvinus University of Budapest
2. Regina Radanovits
Corvinus University of Budapest

Abstract

Many-to-one assignment games (Sotomayor, 1992) are extensions of one-to-one assignment games (Shapley and Shubik, 1972). It is know that the core of many-to-one assignment games is non-empty and has the two side-optimal special vertices. We consider many-to-one assignment games as special linear production games (Owen, 1975) and investigate the Owen core (the set of core allocations obtained from the dual optimal solutions of the LP for the grand coalition). Unlike in assignment games where the two sets coincide, in many-to-one assignment games the dimension of the Owen core is at most the number of players allowed to be assigned to several players of the other type, while the dimension of the core is at most the number of the 1-capacity players.
We show that the Owen core of a many-to-one assignment game can be described as the core of an associated assignment game. This facilitates the application of various results known for the core of assignment games to the Owen core of many-to-one assignment games. For example, based on the graph-theoretic characterization of the two side-optimal core vertices (Solymosi, 2023), we show that the same allocation maximizes the payoffs for all 1-capacity players both in the Owen core and in the core, but the allocation which minimizes all these payoffs in the Owen core need not be an extreme point of the core. We also provide conditions for the coincidence of these minimizing allocations.

Keywords

Status: accepted

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