Rationally inattentive and strategically (Un)sophisticated

Abstract In a game with costly information acquisition, the ability of one player to acquire information directly affects her opponent’s incentives for gathering information. Rational inattention theory then posits the opponent’s information-acquisition strategy is a direct function of these incentives. This paper argues that people are cognitively limited in predicting their opponent’s level of information, and hence lack the strategic sophistication that the theory requires. In an experiment involving a real-effort attention task and a simple two-player trading game, I study the ability of subjects to (1) anticipate the information acquisition of opponents in this strategic game, and (2) best respond to this information acquisition when acquiring their own costly information. I study this by exogenously manipulating the difficulty of the attention task for both the player and their opponent. Predictions of behavior are generated by a novel theoretical model in which Level-K agents can acquire information à la rational inattention. I find an out-sized lack of strategic sophistication, driven largely by the cognitive difficulties of predicting opponent information. These results suggest a necessary integration of the theories of rational inattention and costly sophistication in strategic settings.