Ex-ante Comparative Statics: Responsiveness to Information Quality
An agent chooses an action after acquiring information about an uncertain state. From an ex-ante perspective, the agent's optimal action is an endogenously determined random variable. We study how the quality of information affects the distribution of the optimal action. In particular, we study responsiveness, a comparative statics that captures mean-preserving spreads and second-order stochastic dominance shifts in the distribution of the optimal action. The higher the quality of information, the more closely the agent tailors her actions to the state, and consequently, under conditions we derive on payoffs, the more responsive the optimal action. We extend our results to Bayesian games with strategic complementarities in which different players have information of varying quality. We show that a player's equilibrium actions become more responsive as the quality of an opponent's information improves. We apply the comparative statics of responsiveness to study the demand for information in covert and overt information acquisition games.