Testing the level of consistency between choices and beliefs in games using eye-tracking

We use eye-tracking technique to test whether players’ actions are consistent with their expectations of their opponent’s behavior. Participants play a series of two-player 3 by 3 one shot games and state their beliefs about which actions they expect their counterpart to play (first-order beliefs) or about which actions their counterparts expect them to play (second-order beliefs). We perform a mixed model cluster analysis and classify participants into types according to both their attentional patterns of visual information acquisition and choices. Players classified as strategic (Level-2 players) and players classified as having other-regarding preferences like Inequity aversion and Prosociality exhibit patterns of visual attention and choices that are mainly consistent with their stated beliefs. Conversely, players classified as non-strategic (Level-1, Pessimistic, Optimistic and Competitive) do not best respond to any specific belief, but apply simple decision rules regardless of whether they are playing or stating their beliefs. Thus, using eye-tracking data we could identify a larger consistency between actions and stated beliefs compared with previous studies, and we could characterize the behavioral rules associated with choice-beliefs inconsistency. Implications for the theories of bounded rationality are discussed.