Diffusion mechanism design, which investigate how to incentivise agents to invite as many colleagues to a multi-agent decision making as possible, is a new research paradigm at the intersection between microeconomics and computer science. In this paper we extend traditional facility location games into the model of diffusion mechanism design. Our objective is to completely understand to what extent of anonymity/voter-relevance we can achieve, along with strategy-proofness and Pareto efficiency when voters strategically invite collegues. We define a series of anonymity properties applicable to the diffusion mechanism design model, as well as parameterized voter-relevance properties for guaranteeing reasonably-fair decision making. We obtained two impossibility theorems and two existence theorems, which partially answer the question we have raised in the beginning of the paper

翻译：扩散机制设计是微观经济学与计算机科学交叉领域的一个新兴研究范式，其研究重点在于如何激励智能体在多方决策过程中邀请尽可能多的同行参与。本文在扩散机制设计框架下对传统设施选址博弈进行了扩展。我们的目标是全面理解：当投票者策略性地邀请同行时，在满足策略证明性与帕累托效率的前提下，能够实现何种程度的匿名性/投票者相关性。我们定义了一系列适用于扩散机制设计模型的匿名性属性，以及用于保证决策合理公平性的参数化投票者相关性属性。通过研究，我们得到了两个不可能性定理和两个存在性定理，这些结果部分地回答了本文开头提出的问题。