Measuring Attention and Strategic Behavior in Games with Private Information

Abstract

In experiments, people do not always appear to think very strategically or to infer the information of others from their choices. We report experimental results in games of private information with three information states, which vary in strategic complexity. "Mousetracking" is used to record which game payoffs subjects look at, for how long, to learn more about the thinking process. 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 nonequilibrium 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.

On the persistence of strategic sophistication

“…The Level-k model has also been applied successfully to a variety of other games, including "hide-and-seek" games [27], incomplete-information betting games [11], betting games and matrix games [57], coordinated attack games [48], sender-receiver games augmented with eye-tracking data [65], and cheap-talk games [45]. In the field, Level-k has been shown to fit behavior in Swedish lowest-unique-positive-integer lottery games [55] and to explain the fact that movies that were not released to critics before their public opening earn higher revenues [12].…”

“…The capacity bounds the level, so k i (γ, τ i ) ≤ c i (γ) for all i, γ, and τ i . 11 Let Θ be the space of all possible types. Note that c i does not vary in τ i since the capacity represents a player's underlying ability to "solve" a particular game, regardless of the type of her opponent.…”

Nonparametric learning rules from bandit experiments: the eyes have it!

“…Yoshida and Ishii (2006), Boorman, Behrens, Woolrich, and Rushworth (2009) in the recent fMRI neuroscience literature), mouse-tracking (cf. Brocas, Carrillo, Wang, and Camerer (2009)), or eye movements (as in , and the present paper).…”

A psychological approach to strategic thinking in games

“…CH models predict that level-0 and level-1 thinkers won't understand how this information can guide a player. This leads to interesting phenomena that are not possible in equilibrium analysis, such as dishonest sellers exploiting gullible buyers [31 ,32]; the 'winner's curse,' where bidders can only guess the value of an object (e.g., oil lease auctions), perhaps too optimistically [28,33]; and zero-sum speculation in which two people should never agree to bet each other, but often do [34,35].…”