Traditional sufficient conditions for Nash implementation may fail on Internet

TL;DR

This paper demonstrates that traditional conditions for Nash implementation may fail in internet-based communication channels, as agents can form unobservable, self-enforcing agreements that prevent certain social choice rules from being Nash implementable.

Contribution

It reveals a new failure of Maskin's theorem when agents communicate via channels like the Internet, highlighting the impact of unobservable agreements.

Findings

Agents can form unobservable, self-enforcing agreements

Such agreements prevent certain social choice rules from being Nash implementable

Maskin's theorem may not hold in internet communication scenarios

Abstract

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.