Social Value of Public Information

Social Value of Public Information

92 (2002), 1521-1534 | Stephen Morris and Hyun Song Shin
This appendix discusses extensions and variations of the model in the paper "Social Value of Public Information." It starts with a two-state example where the true state θ is 0 or 1 with equal probability. A public signal is correct with probability q, and each player observes a private signal correct with probability p. Players use a strategy that combines their expectation of the state and the expected action of the other player. The equilibrium conditions are derived, showing that as the parameter r approaches 1, only public information is used. The welfare function is calculated, and it is shown that public information can be damaging under certain conditions. The appendix also considers alternative welfare definitions, where players maximize a general payoff function that includes different weights for losses from distances between actions, the true state, and the average action. The optimal action is derived, and the equilibrium actions are found. The welfare function is expressed in terms of these parameters, and it is shown that public information is always valuable if β = 0. Public information can be damaging when β > 0 and α is low. A variation of the example is considered where each player has a payoff function that includes an externality term. The equilibrium is unchanged, but social welfare is approximately equal to the externality term. For some choice of the externality function, public information may be damaging even in the absence of private information. Finally, the appendix considers a model with correlated private signals, where players can observe many signals, and the signals are multivariate normal.This appendix discusses extensions and variations of the model in the paper "Social Value of Public Information." It starts with a two-state example where the true state θ is 0 or 1 with equal probability. A public signal is correct with probability q, and each player observes a private signal correct with probability p. Players use a strategy that combines their expectation of the state and the expected action of the other player. The equilibrium conditions are derived, showing that as the parameter r approaches 1, only public information is used. The welfare function is calculated, and it is shown that public information can be damaging under certain conditions. The appendix also considers alternative welfare definitions, where players maximize a general payoff function that includes different weights for losses from distances between actions, the true state, and the average action. The optimal action is derived, and the equilibrium actions are found. The welfare function is expressed in terms of these parameters, and it is shown that public information is always valuable if β = 0. Public information can be damaging when β > 0 and α is low. A variation of the example is considered where each player has a payoff function that includes an externality term. The equilibrium is unchanged, but social welfare is approximately equal to the externality term. For some choice of the externality function, public information may be damaging even in the absence of private information. Finally, the appendix considers a model with correlated private signals, where players can observe many signals, and the signals are multivariate normal.
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