Privacy as a coordination game

In Ghosh-Ligett 2013, we propose a simple model where individuals in a privacy-sensitive population with privacy requirements 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. Agents decide whether or not to participate based on how their privacy requirement compares against their expectation of the privacy they will receive. 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 in this game which consist of threshold strategies, where all agents with requirements above 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.