Local Dynamics in Bargaining Networks via Random-Turn Games

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We present a new technique for analyzing the rate of convergence of local dynamics in bargaining networks. The technique reduces balancing in a bargaining network to optimal play in a random-turn game. We analyze this game using techniques from martingale and Markov chain theory. We obtain a tight polynomial bound on the rate of convergence for a nontrivial class of unweighted graphs (the previous known bound was exponential). Additionally, we show this technique extends naturally to many other graphs and dynamics.