Traditional sufficient conditions for Nash implementation may fail on Internet

The Maskin's theorem is a fundamental work in the theory of mechanism design. In this paper, we propose that if agents report messages to the designer through channels (e.g., Internet), agents can construct a self-enforcing agreement such that any Pareto-inefficient social choice rule satisfying monotonicity and no-veto will not be Nash implementable when an additional condition is satisfied. The key points are: 1) The agreement is unobservable to the designer, and the designer cannot prevent the agents from constructing such agreement; 2) The agents act non-cooperatively, and the Maskin mechanism remain unchanged from the designer's perspective.