Title: The assignment game: Decentralized dynamics, rate of convergence, and equitable core selection
We study decentralized learning dynamics for the classic assignment game with transferable utility. At random points in time firms and workers match, break up, and re-match in the search for better opportunities. Agents have no knowledge of other agents’ strategies, payoffs, or the structure of the game, and there is no central authority with such knowledge either. We propose a simple learning process that converges to stable and optimal outcomes (the core). A variant of the process, where sometimes the firms exhibit greater price stickiness than the workers and at other times the reverse holds, is shown to converge in polynomial time. If payoffs are perturbed a subset of the core with a natural equity interpretation is selected.