Bayesian Games with Rationally Inattentive Players

We study how scarcity of attention affects strategic choice behaviour in a 2-player incomplete information entry game. Scarcity of attention is a common psychological character among population (Kahnemann, 1973, Attention and effort, Prentice Hall), and it is modelled by the rational inattention approach introduced by Sims (1998, Carnegie-Rochester Conference Series on Public Policy, 49, 317–356). In this game, players acquire information about their private payoff shocks at a cost, which follows a high-low binary distribution. We find that high information cost can generate multiple equilibria, and the number of equilibria differs with respect to different ranges of information cost. The number of equilibria could be 1, 5 or 3. Increasing the information cost could encourage or discourage a player to choose entry in some equilibria. This depends on whether the prior probability of high payoff shocks is greater than a given threshold value. We also exhibit a necessary and sufficient condition of parameter specification such that with the same set of parameters satisfying this condition, both the rational inattention Bayesian game and a Bayesian quantal response equilibrium game where the observation errors are additive and follow a Type-I extreme value distribution can have a common equilibrium. JEL: C72, D91