CFDP 2299R2

Learning Efficiency of Multi-Agent Information Structures

Publication Date: August 2021

Revision Date: December 2021July 2022

Pages: 50

Abstract: 

We study which multi-agent information structures are more effective at eliminating both first-order and higher-order uncertainty, and hence at facilitating efficient play in incomplete-information coordination games. We consider a learning setting à la Cripps, Ely, Mailath, and Samuelson (2008) where players have access to many private signal draws from an information structure. First, we characterize the rate at which players achieve approximate common knowledge of the state, based on a simple learning efficiency index. Notably, this coincides with the rate at which players’ first-order uncertainty vanishes, as higher-order uncertainty becomes negligible relative to first-order uncertainty after enough signal draws. Based on this, we show that information structures with higher learning efficiency induce more efficient equilibrium outcomes in coordination games that are played after sufficiently many signal draws. We highlight some robust

Keywords: higher-order beliefs, common learning, coordination, speed of learning, comparison of information structures