Cheap Talk with Strategic Substitutability

In the classic Crawford-Sobel (CS) model of strategic communication between an informed Sender and uninformed Receiver, perfect information transmission is never achieved as an equilibrium outcome. I present a modified version of the CS cheap talk game with the following two innovations: (i) both players take actions, and (ii) actions are strategic substitutes. In contrast to the CS setup, the modified game can facilitate perfect information revelation. I characterize the conditions under which a full information revelation equilibrium exists. When these conditions are violated, only partial revelation equilibria exist. Under partial revelation, the Sender reveals information only up to a threshold state and pools beyond this threshold, resulting in some loss of information. Welfare analysis suggests that partial revelation equilibria with a higher threshold pareto dominate those with lower thresholds. Crucially, a higher threshold equilibrium is also interim efficient – every Sender type (weakly) prefers this over a lower threshold equilibrium.