Information Acquisition, Efficiency, and Non-fundamental Volatility

This paper analyzes non-fundamental volatility and efficiency in a class of large games (including e.g. linear-quadratic beauty contests) that feature strategic interaction and endogenous information acquisition. We adopt the rational inattention approach to information acquisition but generalize to a large class of information costs. Agents may learn not only about exogenous states, but also about endogenous outcomes. We study how the properties of the agents' information cost relate to the properties of equilibria in these games. We provide the necessary and sufficient conditions information costs must satisfy to guarantee zero non-fundamental volatility in equilibrium, and provide another set of necessary and sufficient conditions to guarantee equilibria are efficient. We show in particular that mutual information, the cost function typically used in the rational inattention literature, both precludes non-fundamental volatility and imposes efficiency, whereas the Fisher information cost introduced by Hebert and Woodford [2020] generates both non-fundamental volatility and inefficiency.