Sealed-bid auctions are a common way of allocating an asset among a set of parties but require trusting an auctioneer who analyses the bids and determines the winner. Many privacy-preserving computation protocols for auctions have been proposed to eliminate the need for a trusted third party. However, they lack fairness, meaning that the adversary learns the outcome of the auction before honest parties and may choose to make the protocol fail without suffering any consequences. In this work, we propose efficient protocols for both first and second-price sealed-bid auctions with fairness against rational adversaries, leveraging secret cryptocurrency transactions and public smart contracts. In our approach, the bidders jointly compute the winner of the auction while preserving the privacy of losing bids and ensuring that cheaters are financially punished by losing a secret collateral deposit. We guarantee that it is never profitable for rational adversaries to cheat by making the deposit equal to the bid plus the cost of running the protocol, i.e., once a party commits to a bid, it is guaranteed that it has the funds and it cannot walk away from the protocol without forfeiting the bid. Moreover, our protocols ensure that the winner is determined and the auction payments are completed even if the adversary misbehaves so that it cannot force the protocol to fail and then rejoin the auction with an adjusted bid. In comparison to the state-of-the-art, our constructions are both more efficient and furthermore achieve stronger security properties, i.e., fairness. Interestingly, we show how the second-price can be computed with a minimal increase of the complexity of the simpler first-price case. Moreover, in case there is no cheating, only collateral deposit and refund transactions must be sent to the smart contract, significantly saving on-chain storage.