Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept used in social choice theory. However, we argue that this concept has serious drawbacks. In particular, many strategy-proof mechanisms have a continuum of Nash equilibria, some of which produce the wrong outcome. A possible solution to this problem is to require double implementation in dominant strategy equilibria and in Nash equilibria, called secure implementation. We conducted experiments on two strategy-proof mechanisms. One of them is not secure with many bad Nash equilibria, whereas the other secure mechanism has a unique good Nash equilibrium. We observed subjects adopted dominant strategies significantly less often in the non-secure mechanism than in the secure mechanism.
