Information and beliefs in a repeated normal-form game

We study beliefs and choices in a repeated normal-form game. In addition to a baseline treatment with common knowledge of the game structure and feedback about choices in the previous period, we run treatments (i) without feedback about previous play, (ii) with no information about the opponent's payoffs and (iii) with random matching. Using Stahl and Wilson's (1995) model of limited strategic reasoning, we classify behavior with regard to its strategic sophistication and consider its development over time. We use belief statements to check for the consistency of subjects' actions with the stated beliefs as well as for the accuracy of their beliefs (relative to the opponent's true choice). In the baseline treatment we observe more sophisticated play as well as more accurate beliefs and more best responses to beliefs over time. We isolate feedback as the main driving force of learning to play strategically and to form beliefs that accurately predict the behavior of the opponent.