Best-Reply Mechanisms

In many real-world settings, strategic agents are instructed to follow best-reply dynamics (economic markets, Internet protocols, etc.). Such settings give rise to many questions: Will best-reply dynamics “converge” or go on indefinitely? Will they converge quickly? What happens in distributed and asynchronous settings in which communication between players may be delayed or lost? Is it in the best interest of the agents to follow best-reply dynamics? We show that, for a superclass of dominance-solvable games, best-reply dynamics converge within polynomial time to a pure Nash equilibrium. Moreover, we show that convergence is assured even in asynchronous settings. We then study best-reply dynamics in the context of mechanism design. We characterize a narrower subclass of games for which we prove that best-reply dynamics are ex-post-Nash incentive-compatible. We provide several examples of such games: stable-roommates problems, network-routing games, first-price auctions, and congestion-control games. ∗The School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel. Google, Tel Aviv, Israel. Supported by grants from the Israel Science Foundation. E-mail: [email protected] †The School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel. Supported by grants from the Israel Science Foundation. E-mail: [email protected] ‡The School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel. Supported by grants from the Israel Science Foundation. E-mail: [email protected]