Truthful Mechanisms for Agents that Value Privacy

Details Truthful Mechanisms for Agents that Value Privacy Truthful Mechanisms for Agents that Value Privacy

2011-11-23

arxiv.org/abs/1111.5472v1

Computer Science

Computer Science and Game Theory

Scientific paper

A recent paper of Xiao (Cryptology ePrint Technical Report, May 2011) constructs economic mechanisms that are simultaneously truthful and differentially private, improving previous results of McSherry and Talwar (FOCS 2007) and Nissim, Smorodinsky, and Tennenholtz (CoRR, April 2010 and ITCS 2012). Xiao's paper also argues that this conjunction of truthfulness and differential privacy may not be sufficient to elicit truthful behavior from player that value privacy. Specifically, he gives an example of a mechanism that is truthful and differentially private, but where truthfulness is lost if one includes a particular measure of privacy cost in the players' utility functions (namely, mutual information between the player's type and the outcome). In this paper: We propose a new, more general way of modelling privacy in players' utility functions. Specifically, we only assume that if an outcome $o$ has the property that any report of player $i$ would have led to $o$ with approximately the same probability, then $o$ has small privacy cost to player $i$. We give three mechanisms that are truthful with respect to our modelling of privacy: for an election between two candidates, for a discrete version of the facility location problem, and for a general social choice problem with discrete utilities (via a VCG-like mechanism). As the number $n$ of players increases, the social welfare achieved by our mechanisms approaches optimal (as a fraction of $n$)

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