Figure 1.

(a) Graphical illustration of the Cognitive Hierarchy (CH) model. CH models the strategy space of players through a hierarchical structure characterized by increasing levels of strategic sophistication. The hierarchy starts with players who play randomly and do not form any beliefs about the choices of their counterparts (level-0). The second level in the hierarchy predicts level-1 players, who best respond to the belief that the counterparts are level-0; then CH predicts level-2 players, who best respond to the belief that the population of potential opponents is a mixture between level-0 and level-1, and so on, increasing the number of steps of strategic sophistication. (b) Experimental task. Participants were tested in groups. Every participant underwent three consecutive experimental phases (Assessment, Observation and Re-Assessment). In all phases, participants played one-shot 3 × 3 normal form games with a computer algorithm (PC) with fixed but unknown behavior (level-1 strategy). Participants played as row player and had to select one of the three rows of the game matrix, whereas the artificial agent played as column player and chose one of the matrix columns. The combination of the two players’ choices determined the game outcome (green payoff for the participant, red payoff for the artificial agent). Participants did not receive feedback on the game outcomes. In the Observation phase, participants received feedback on the choices of the best player in the Assessment phase (the model). The feedback consisted in a black arrow in correspondence to the row selected by the model. (c) Experimental design. Participants in a specific experimental session were assigned to one of three experimental treatments (No-feedback, Pre-feedback, Post-feedback). The Assessment phase was identical for all the experimental treatments: participants played 22 one-shot games with the same artificial agent, without any feedback. Then participants in all treatments were told if they were the best player in the session (or not). In the Observation phase, participants received different types of feedback based on the experimental treatment. In the Pre-feedback treatment, participants could observe the decision taken by the model (the best player in the Assessment phase) in that game as soon as the game matrix appeared, before they made their choice. Conversely, participants in the Post-feedback treatment could see the model’s feedback only after they made their decision. In the No-feedback treatment, participants did not receive any feedback on the model’s choices. Eventually, participants in all treatments underwent the Re-assessment phase, in which they played 22 new games without receiving the model’s feedback, as in the Assessment phase.