Random Paths to Pairwise Stability in Many-to-Many Matching Problems: A Study on Market Equilibration

Fuhito Kojima, M. Utku Ünver
2006 Social Science Research Network  
This paper considers a decentralized process in many-to-many matching problems. We show that if agents in one side of the market have substitutable preferences and those in the other side have responsive preferences, then there exists a finite path of matchings such that (i) each matching in the path is formed by satisfying a blocking individual or a blocking pair for the previous matching and (ii) the final matching is pairwise-stable. This implies that an associated stochastic process
more » ... tic process converges: A stochastic process converges to a pairwise-stable matching in finite time with probability one, if each blocking individual or pair is satisfied with a positive probability at each period along the process.
doi:10.2139/ssrn.888640 fatcat:62ulsn6pi5gcbixzx4bat7xo4a