Estimating Hidden Markov Models (HMMs) of the cognitive process in strategic thinking using eye-tracking - Li, Xiaomin; Henning, Thomas; Camerer, Colin (Frontiers in Behavioral Economics, 2023)
Hidden Markov Models (HMMs) are used to study language, sleep, macroeconomic states, and other processes that reflect probabilistic transitions between states that can't be observed directly. This paper applies HMMs to data from location-based game theory experiments. In these location games, players choose a pixel location from an image. These players either have a common goal (choose a matching location), or competing goals, to mismatch (hide) or match (seek) in hider-seeker games. We use eye-tracking to record where players look throughout the experimental decision. Each location's numerical salience is predicted using an accurate, specialized vision science-based neural network [the Saliency Attentive Model (SAM)]. The HMM shows the pattern of transitioning from hidden states corresponding to either high or low-salience locations, combining the eye-tracking and salience data. The transitions vary based on the player's strategic goal. For example, hiders transition more often to low-salience states than seekers do. The estimated HMM is then used to do two useful things. First, a continuous-time HMM (cHMM) predicts the salience level of each player's looking over several seconds. The cHMM can then be used to predict what would happen if the same process was truncated by time pressure: This calculation makes a specific numerical prediction about how often seekers will win, and it predicts an increase in win rate but underestimates the size of the change. Second, a discrete-time HMM (dHMM) can be used to infer levels of strategic thinking from high-to-low salience eye-tracking transitions. The resulting estimates are more plausible than some maximum-likelihood models, which underestimate strategic sophistication in these games. Other applications of HMM in experimental economics are suggested.