Incentive-compatible simple mechanisms

We consider mechanisms for allocating a fixed amount of divisible resources among multiple agents when they have quasilinear preferences and can only report messages in a one-dimensional space. We show that in contrast with infinite-dimensional message spaces, efficiency is neither compatible with implementation in dominant strategies nor compatible with implementation in Bayesian Nash equilibrium. However, for the weaker notion of implementation, such as in the Nash equilibrium, we find that a class of 'VCG-like' mechanisms is the only efficient selection in one-dimensional message spaces. The trifecta in mechanism design, namely efficiency, fairness, and simplicity of implementation, is achieved via a mechanism that we introduce and characterize in this paper.