We analyze a class of games with interdependent values and linear best responses. The payoﬀ uncertainty is described by a multivariate normal distribution that includes the pure common and pure private value environment as special cases. We characterize the set of joint distributions over actions and states that can arise as Bayes Nash equilibrium distributions under any multivariate normally distributed signals about the payoﬀ states. We characterize maximum aggregate volatility for a given distribution of the payoﬀ states. We show that the maximal aggregate volatility is attained in a noise-free equilibrium in which the agents confound idiosyncratic and common components of the payoﬀ state, and display excess response to the common component. We use a general approach to identify the critical information structures for the Bayes Nash equilibrium via the notion of Bayes correlated equilibrium, as introduced by Bergemann and Morris (2013b).
Bergemann, Dirk; Heumann, Tibor; and Morris, Stephen, "Information, Interdependence, and Interaction: Where Does the Volatility Come From?" (2013). Cowles Foundation Discussion Papers. 2323.