Secure Implementation

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept in social choice theory. However, this concept has serious drawbacks. In particular, many strategy-proof mechanisms have multiple Nash equilibria, some of which produce the wrong outcome. A possible solution to this problem is to require double implementation in Nash equilibrium and in dominant strategies, i.e., secure implementation. We characterize securely implementable social choice functions, and compare our results with dominant strategy implementation. In standard quasi-linear environments with divisible private or public goods, there exist Pareto efficient (non-dictatorial) social choice functions that can be securely implemented. But in the absence of side-payments, secure implementation is incompatible with Pareto efficiency.