Essays on Privacy, Information, and Anonymous Transactions

This dissertation uses game theoretic models to examine the effects of agent anonymity on markets for goods and for information. In open, anonymous settings, such as the Internet, anonymity is relatively easy to obtain --- oftentimes another email address is sufficient. By becoming anonymous, agents can participate in various mechanisms (such as elections, opinion polls, auctions, etc.) multiple times. The first chapter (joint work with Vincent Conitzer) studies elections that disincentivize voters from voting multiple times. A voting rule is false-name-proof if no agent ever benefits from casting additional votes. In elections with two alternatives, it is shown that there is a unique false-name-proof voting rule that is most responsive to votes. The probability that this rule selects the majority winner converges to 1 as the population grows large. Methods to design analogous rules for elections with 3 or more alternatives are proposed. The second chapter (also joint work with Vincent Conitzer) extends the analysis in the first chapter to broader mechanism design settings, where the goal is to disincentivize agents from participating multiple times. The cost model from the first chapter is generalized and revelation principles are proven. The third chapter studies a setting where firms are able to recognize their previous customers, and may use information about consumers' purchase histories to price discriminate (which may incentivize consumers to be anonymous). The formal model considers a monopolist and a continuum of heterogeneous consumers, where consumers are able to maintain their anonymity at some cost. It is shown that when consumers can costlessly maintain their anonymity, they all individually choose to do so, which paradoxically results in the highest profit for the monopolist. Increasing the cost of anonymity can benefit consumers, but only up to a point; at that point, the effect is reversed. Some of the results are extended to a setting with two competing firms selling differentiated products. Finally, the cost of maintaining anonymity is endogenized by considering a third party that can make consumers anonymous for a fee of its choosing. It is shown that this third party would prefer to be paid by the firm for allowing consumers to costlessly maintain their anonymity.