Evolutionary Dynamics and Fast Convergence in the Assignment Game
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 sesarch for better opportunities.� We propose a simple learning process in which players have no knowledge about other players' payoffs or actions and they update their behavior in a myopic fashion.� Behavior fluctuates according to a random variable that reflects current market conditions: sometimes the firms exhibit greater price stickiness than the workers, and at other times the reverse holds.� We show that this stochastic learning process converges in polynomial time to the core.� While convergence to the core is known for some types of decentralized dynamics this paper is the first to prove fast convergence, a crucial feature from a practical standpoint.� The proof relies on novel results for random walks on graphs, and more generally suggests a fruitful connection between the theory of random walks and matching theory.
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