The Power of Randomness in Bayesian Optimal Mechanism Design

摘要

We investigate the power of randomness in the context of a fundamental Bayesian optimal mechanism design problem— a single seller aims to maximize expected revenue by allocating multiple kinds of resources to "unit-demand" agents with preferences drawn from a known distribution. When the agents' preferences are single-dimensional Myerson's seminal work [14] shows that randomness offers no benefit—the optimal mechanism is always deterministic. In the multidimensional case, where each agent's preferences are given by different values for each of the available services, Briest et al. [6] recently showed that the gap between the expected revenue obtained by an optimal randomized mechanism and an optimal deterministic mechanism can be unbounded even when a single agent is offered only 4 services. However, this large gap is attained through unnatural instances where values of the agent for different services are correlated in a specific way. We show that when the agent's values involve no correlation or a specific kind of positive correlation, the benefit of randomness is only a small constant factor (4 and 8 respectively). Our model of positively correlated values (that we call the common base value model) is a natural model for unit-demand agents and items that are substitutes. Our results extend to multiple agent settings as well.