The Price of Uncertainty

We study the degree to which small fluctuations in costs in well-studied potential games can impact the result of natural best-response and improved-response dynamics. We call this the Price of Uncertainty and study it in a wide variety of potential games (including fair cost-sharing games, set-cover games, routing games, and job-scheduling games), finding a number of surprising results. In particular, we show that in certain cases, even extremely small fluctuations can cause these dynamics to spin out of control and move to states of much higher social cost, whereas in other cases these dynamics are much more stable even to large degrees of fluctuation. We also consider the resilience of these dynamics to a small number of Byzantine players about which no assumptions are made. We show again a contrast between different games. In certain cases (e.g., fair cost-sharing, set-covering, job-scheduling) even a single Byzantine player can cause best-response dynamics to transition to states of substantially higher cost, whereas in others (e.g., the class of beta-nice games which includes routing, market-sharing and many others) these dynamics are much more resilient.

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