Learning Efficiency of Multiagent Information Structures

Which information structures are more effective at eliminating first-and higher-order uncertainty and hence at facilitating efficient play in coordination games? We consider a learning setting where players observe many private signals about the state. First, we characterize multi-agent learning efficiency, that is, the rate at which players approximate common knowledge. We find that this coincides with the rate at which first-order uncertainty disappears, as higher-order uncertainty vanishes faster than first-order uncertainty. Second, we show that with enough signal draws, information structures with higher learning efficiency in-duce higher equilibrium welfare. We highlight information design implications for games in data-rich environments.