Paths to stable allocations

Arbeitspapier

The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case of uncoordinated processes in stable allocation instances. In this setting, a feasible allocation is given and the aim is to reach a stable allocation by raising the value of the allocation along blocking edges and reducing it on worse edges if needed. Do such myopic changes lead to a stable solution? In our present work, we analyze both better and best response dynamics from an algorithmic point of view. With the help of two deterministic algorithms we show that random procedures reach a stable solution with probability one for all rational input data in both cases. Surprisingly, while there is a polynomial path to stability when better response strategies are played (even for irrational input data), the more intuitive best response steps may require exponential time. We also study the special case of correlated markets. There, random best response strategies lead to a stable allocation in expected polynomial time.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: IEHAS Discussion Papers ; No. MT-DP - 2018/20

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Computational Techniques; Simulation Modeling ; Bargaining Theory; Matching Theory
• Thema: stable matching ; stable allocation ; paths to stability ; best response strategy ; better response strategy ; correlated market

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Cseh, Ágnes ; Skutella, Martin
• Ereignis: Veröffentlichung
• (wer): Hungarian Academy of Sciences, Institute of Economics
• (wo): Budapest
• (wann): 2018

Weitere Informationen

• Handle: http://hdl.handle.net/10419/222033
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ