Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
We study the reasoning process in an environment where final choices are well understood and the associated theory is procedural by introducing two-person beauty contest games played spatially on two-dimensional grid maps. Players choose locations and are rewarded by hitting targets dependent on opponents' choice locations. By tracking subjects' eye movements (lookups), we infer their reasoning process and classify subjects into various levels. More than a half of the subjects' classifications coincides with their classifications using final choices, supporting a literal interpretation of the level-k model for subject's reasoning process. Lookup analyses reveal that the center area is where most subjects initially look at. This sheds light on the level-0 belief. Moreover, learning lookups of a trial on average could increase payoffs of that trial and eliminates roughly 60% of the gap to empirical best response, indicating how valuable lookups can help predict choices.