Game Forms with Minimal Message Spaces
研究在纳什均衡下实现绩效标准所需的最小通信量，证明在交换经济中实现瓦尔拉斯配置的最小消息空间维度约为 n(l-1)+l/(n-1)，并构造了达到该维度的机制。
This paper is concerned with the amount of communication that must be provided to implement a performance standard by a mechanism whose stationary messages have the Nash property. We study the question whether a given message space is large enough to implement a given performance standard. In general, an implementing mechanism with the Nash property in messages requires a larger message space than suffices for decentralized realization without regard to individual incentives. In particular, we study implementation of Walrasian allocations in exchange environments. We show that the smallest message space that implements Walrasian allocations is one of dimension, roughly, n (1 - 1) + I/(n - 1), where I is the number of commodities and n the number of agents. We exhibit an implementing mechanism whose message space has that dimension.