A contract signing protocol lets two people exchange digital signatures on a pre-agreed text. Optimistic contract signing protocols enable signers to do so without invoking a third party. However, an adjudicating party remains available should one or both signers need timely resolution. We analyze optimistic contract signing protocols using a game-theoretic approach and prove a fundamental impossibility result: in any fair, optimistic, timely protocol, an optimistic player yields an advantage to a strategic opponent. This is joint work with John Mitchell, Andre Scedrov and Vitaly Shmatikov. If time permits, I shall discuss some work on multi-party contract signing protocols.