Privacy and coordination: computing on databases with endogenous participation

We propose a simple model where individuals in a privacy-sensitive population decide whether or not to participate in a pre-announced noisy computation by an analyst, so that the database itself is endogenously determined by individuals' participation choices. The privacy an agent receives depends both on the announced noise level, as well as how many agents choose to participate in the database. Each agent has some minimum privacy requirement, and decides whether or not to participate based on how her privacy requirement compares against her expectation of the privacy she will receive if she participates in the computation. This gives rise to a game amongst the agents, where each individual's privacy if she participates, and therefore her participation choice, depends on the choices of the rest of the population. We investigate symmetric Bayes-Nash equilibria, which in this game consist of threshold strategies, where all agents whose privacy requirements are weaker than a certain threshold participate and the remaining agents do not. We characterize these equilibria, which depend both on the noise announced by the analyst and the population size; present results on existence, uniqueness, and multiplicity; and discuss a number of surprising properties they display.