Convergence of Ordered Improvement Paths in Generalized Congestion Games
We consider generalized congestion games, a class of games in which players share a set of strategies and the payoff functions depend only on the chosen strategy and the number of players playing the same strategy, in such a way that fewer such players results in greater payoff. In these games we consider improvement paths. As shown by Milchtaich  such paths may be infinite. We consider paths in which the players deviate in a specific order, and prove that ordered best response improvement paths are finite, while ordered better response improvement paths may still be infinite.
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