Measuring attention and strategic behavior in games with private information

In experiments, people do not always appear to think very strategically or to infer the information of others from their choices. To understand this thinking process further, we use "Mousetracking" to record which game payoffs subjects look at, for how long, in games of private information with three information states, which vary in strategic complexity. Subjects often deviate from Nash equilibrium choices, converge only modestly toward equilibrium across 40 trials, and often fail to look at payoffs which they need to in order to compute an equilibrium response. Theories such as QRE and cursed equilibrium, which can explain non-equilibrium choices, are not well supported by the combination of both choices and lookups. When cluster analysis is used to group subjects according to lookup patterns and choices, the clusters appear to correspond approximately to level-3, level-2 and level-1 thinking in level-k cognitive hierarchy models. The connection between looking and choices is strong enough that the time durations of looking at key payoffs can predict choices, to some extent, at the individual level and at the trial-by-trial level.