Hidden Markov Modeling of the Cognitive Process in Strategic Thinking

Hidden Markov models (HMMs) are used to study language, sleep, and other processes that reflect probabilistic transitions between states that cannot be observed directly. We apply HMMs to data from experiments on visual location games. In these games, people choose a pixel from an image. They either have a common goal to match locations or have different goals in hider-seeker games. Eyetracking records where they look at a fine-grained time scale. Numerical salience of different locations is predicted, a priori, from a specialized vision science based neural network. The HMM shows the pattern of transitioning from hidden states corresponding to either high or low salience locations, using 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 the course of several seconds. The cHMM is then used to predict what would happen if the same process was truncated by time pressure choosing in two seconds instead of six, cHMM predicts seekers will match hiders 12% of the time; they actually match 15%. Second, dHMM is used to infer levels of strategic thinking from high-to-low transitions (a la Costa-Gomes et al. 2001 and others). The resulting estimates are more plausible than some maximum-likelihood procedures and models which appear to grossly underestimate strategic sophistication. Other applications of HMM in experimental economics are suggested.