Communication complexity and stability of equilibria in economies and games

The theory of decentralized allocation mechanisms introduced by Leonid Hurwicz enabled economists to analyze the implications of requiring an allocation mechanism to perform well over a range of possible economic environments. One of the earliest major results in this theory was the formalization and proof of Hayek's famous assertion that the competitive market mechanism minimizes the communication needed to achieve Pareto efficient allocations. The informational efficiency theorem spawned a large literature on communication complexity in allocation mechanisms. This paper provides an exposition of some results on the communication required to make equilibria locally stable, and the possibility of eliciting the required communication in allocation mechanisms and games.