We study the value of data privacy in a game-theoretic model of trading private data, where a data collector purchases private data from strategic data subjects (individuals) through an incentive mechanism. The private data of each individual represents her knowledge about an underlying state, which is the information that the data collector desires to learn. Different from most of the existing work on privacy-aware surveys, our model does not assume the data collector to be trustworthy. Then, an individual takes full control of its own data privacy and reports only a privacy-preserving version of her data.
In this paper, the value of $\epsilon$ units of privacy is measured by the minimum payment of all nonnegative payment mechanisms, under which an individual's best response at a Nash equilibrium is to report her data in an $\epsilon$-locally differentially private manner. The higher $\epsilon$ is, the less private the reported data is. We derive lower and upper bounds on the value of privacy which are asymptotically tight as the number of data subjects becomes large. Specifically, the lower bound assures that it is impossible to use lower payment to buy $\epsilon$ units of privacy, and the upper bound is given by an achievable payment mechanism that we designed. Based on these fundamental limits, we further derive lower and upper bounds on the minimum total payment for the data collector to achieve a given learning accuracy target, and show that the total payment of the designed mechanism is at most one individual's payment away from the minimum.
We model and analyze cardinal contests, where a principal running a rank-order tournament has access to an absolute measure of the quality of agents' submissions in addition to their relative rankings. We show that a mechanism that compares each agent's output quality against a threshold to decide whether to award her the prize corresponding to her rank is optimal amongst the set of all mixed cardinal-ordinal mechanisms where the j-th ranked submission receives a fraction of the j-th prize that is a non-decreasing function of the submission's quality. Furthermore, the optimal threshold mechanism uses exactly the same threshold for each rank.
Performing interventions is a major challenge in economic policy-making. We propose causal strategic inference as a framework for conducting interventions and apply it to large, networked microfinance economies. The basic solution platform consists of modeling a microfinance market as a networked economy, learning the parameters of the model from the real-world microfinance data, and designing algorithms for various causal questions. For a special case of our model, we show that an equilibrium point always exists and that the equilibrium interest rates are unique. For the general case, we give a constructive proof of the existence of an equilibrium point. Our empirical study is based on the microfinance data from Bangladesh and Bolivia, which we use to first learn our models. We show that causal strategic inference can assist policy-makers by evaluating the outcomes of various types of interventions, such as removing a loss-making bank from the market, imposing an interest-rate cap, and subsidizing banks.
The focus of classic mechanism design has been on truthful direct-revelation mechanisms. In the context of combinatorial auctions the truthful direct-revelation mechanism that maximizes social welfare is the VCG mechanism. For many valuation spaces computing the allocation and payments of the VCG mechanism, however, is a computationally hard problem. We thus study the performance of the VCG mechanism when bidders are forced to choose bids from a subspace of the valuation space for which the VCG outcome can be computed efficiently. We prove improved upper bounds on the welfare loss for restrictions to additive bids and upper and lower bounds for restrictions to non-additive bids. These bounds show that the welfare loss increases in expressiveness. All our bounds apply to equilibrium concepts that can be computed in polynomial time as well as to learning outcomes.