## Cryptology ePrint Archive: Report 2008/418

Privacy-Enhancing First-Price Auctions Using Rational Cryptography

Peter Bro Miltersen and Jesper Buus Nielsen and Nikos Triandopoulos

Abstract: We consider enhancing a sealed-bid single-item auction with \emph{privacy} concerns, our assumption being that bidders primarily care about monetary payoff and secondarily worry about exposing information about their type to other players and learning information about other players' types. To treat privacy explicitly within the game theoretic context, we put forward a novel \emph{hybrid utility} model that considers both fiscal and privacy components in the players' payoffs.

We show how to use rational cryptography to approximately implement a given \emph{ex interim} individually strictly rational equilibrium of such an auction (or any game with a winner) without a trusted mediator through a cryptographic protocol that uses only point-to-point authenticated channels between the players. By ex interim individually strictly rational'' we mean that, given its type and before making its move, each player has a strictly positive expected utility, i.e., it becomes the winner of the auction with positive probability. By approximately implement'' we mean that, under cryptographic assumptions, running the protocol is a computational Nash equilibrium with a payoff profile negligibly close to the original equilibrium.

In addition the protocol has the stronger property that no collusion, of any size, can obtain more by deviating in the implementation than by deviating in the ideal mediated setting which the mechanism was designed in. Also, despite the non-symmetric payoffs profile, the protocol always correctly terminates.

Category / Keywords: cryptographic protocols / rational cryptography