Endogenous information acquisition in Bayesian games with strategic complementarities
This paper studies covert (or hidden) information acquisition in common value Bayesian games of strategic complementarities. Using the supermodular stochastic order to arrange the structures of information increasingly in terms of preferences, we provide novel, easily interpretable and verifiable, though restrictive conditions under which the value of information is increasing and convex, and study the implications in terms of the equilibrium configuration. Increasing marginal returns to information leads to extreme behavior in that agents opt either for the highest or the lowest quality signal, so that the final analysis of this complex game simplifies greatly into that of a two-action game. This result can rationalize the complete information game as an endogenous outcome. Finally, we also establish that higher-quality information leads players to select more dispersed actions in the Bayesian game.