In this work, we construct a second price (Vickrey) auction protocol (SPA), which does not require any auctioneers and ensures total privacy in the presence of rational parties participating in the auction. In particular, the confidentiality of the highest bid and the identity of the second highest bidder are protected. We model the bidders participating in the second price auction as rational, computationally bounded and privacy-sensitive parties. These are self-interested agents who care about winning the auction more than learning about the private bids of other parties. A rational party does not deviate from the protocol arbitrarily but does so only for its own individual 'advantage' -- without any consideration for others. Such an advantage is modelled using suitable utility functions.

Sealed bid auctions are used to allocate a resource among a set of interested parties. Traditionally, auctions need the presence of a trusted auctioneer to whom the bidders provide their private bid values. Existence of such a trusted party is not an assumption easily realized in practice. Generic secure computation protocols can be used to remove a trusted party. However, generic techniques result in inefficient protocols, and typically do not provide fairness -- that is, a corrupt party can learn the output and abort the protocol thereby preventing other parties from learning the output.