Abstract
We study the dynamics of stable marriage and stable roommates markets. Our main tool is the incremental algorithm of Roth and Vande Vate and its generalization by Tan and Hsueh. Beyond proposing alternative proofs for known results, we also generalize some of them to the nonbipartite case. In particular, we show that the lastcomer gets his best stable partner in both incremental algorithms. Consequently, we confirm that it is better to arrive later than earlier to a stable roommates market. We also prove that when the equilibrium is restored after the arrival of a new agent, some agents will be better off under any stable solution for the new market than at any stable solution for the original market. We also propose a procedure to find these agents.
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