This appendix examines extensions and variations of the model discussed in the main paper, focusing on a two-state example and alternative welfare definitions. In the two-state example, the state \(\theta\) takes values 0 and 1 with equal probability, and a binary public signal is correct with probability \(q\) and incorrect with probability \(1 - q\). Each player observes a private signal with a correct probability \(p\). The appendix derives the equilibrium actions for both players and analyzes the welfare implications under different conditions. For the two-state example, the appendix provides expressions for the equilibrium actions and welfare, showing that public information can be beneficial or detrimental depending on the parameters \(r\), \(p\), and \(q\). Specifically, public information is damaging if certain conditions on \(r\), \(p\), and \(q\) are met. The appendix also derives the socially optimal strategy and compares it to the equilibrium actions. In the alternative welfare definitions section, the appendix generalizes the payoff function for players and welfare functions. It considers a more complex payoff function that includes different weights for losses arising from distances between actions, the average action, and the true state. The appendix derives the equilibrium actions and welfare expressions, showing that public information can be valuable or detrimental under certain conditions. The appendix concludes with a detailed derivation of the equilibrium actions and welfare for a specific case where the public signal is conditionally independent of the private signals.This appendix examines extensions and variations of the model discussed in the main paper, focusing on a two-state example and alternative welfare definitions. In the two-state example, the state \(\theta\) takes values 0 and 1 with equal probability, and a binary public signal is correct with probability \(q\) and incorrect with probability \(1 - q\). Each player observes a private signal with a correct probability \(p\). The appendix derives the equilibrium actions for both players and analyzes the welfare implications under different conditions. For the two-state example, the appendix provides expressions for the equilibrium actions and welfare, showing that public information can be beneficial or detrimental depending on the parameters \(r\), \(p\), and \(q\). Specifically, public information is damaging if certain conditions on \(r\), \(p\), and \(q\) are met. The appendix also derives the socially optimal strategy and compares it to the equilibrium actions. In the alternative welfare definitions section, the appendix generalizes the payoff function for players and welfare functions. It considers a more complex payoff function that includes different weights for losses arising from distances between actions, the average action, and the true state. The appendix derives the equilibrium actions and welfare expressions, showing that public information can be valuable or detrimental under certain conditions. The appendix concludes with a detailed derivation of the equilibrium actions and welfare for a specific case where the public signal is conditionally independent of the private signals.