Circumventing the Price of Anarchy: Leading Dynamics to Good Behavior
Maria-Florina Balcan, Avrim Blum and Yishay Mansour
In: ICS 2010(2010).

Abstract

Many natural games can have a dramatic difference between the quality of their best and worst Nash equilibria, even in pure strategies. In such cases one would hope that even if behavior begins at a poor equilibrium, agents with some knowledge of the game would be able to nonetheless find their way to higher quality states. In this work we use a machine learning theory perspective to study how such a process might occur. We develop techniques for understanding and influencing the behavior of natural dynamics in games with multiple equilibria, some of which may be of much higher social quality than others. The key questions we tackle are: Can one assist these dynamics in reaching good equilibria or good behavior? Can one provide natural feature information to learning algorithms that allow them to avoid low-quality equilibria? What kinds of guarantees on the quality of final behavior can we give? We consider two natural learning models in which players choose between greedy behavior and following a proposed good but untrusted strategy and analyze two important classes of games in this context, fair cost-sharing and conensus games. Both games have extremely high Price of Anarchy and yet we show that behavior in these models can efficiently reach low-cost states.

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