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 multiagent 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 induce higher equilibrium welfare. We highlight information design implications for games in data-rich environments.