Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/222033 
Year of Publication: 
2018
Series/Report no.: 
IEHAS Discussion Papers No. MT-DP - 2018/20
Publisher: 
Hungarian Academy of Sciences, Institute of Economics, Budapest
Abstract: 
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.
Subjects: 
stable matching
stable allocation
paths to stability
best response strategy
better response strategy
correlated market
JEL: 
C63
C78
Document Type: 
Working Paper

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