Learning, Persistence, and Transfer of Strategic Sophistication in Games

Abstract

This paper studies the learning, persistence, and transfer of strategic sophistication in interactive games. Prior work has shown that strategic sophistication — understood as the depth of higher-order reasoning a player actually performs — can be enhanced through targeted feedback. What remains unclear is whether such improvements persist over time and whether they generalize across strategically distinct environments.

To address this knowledge gap, we designed and ran a longitudinal experiment combining incentivized choices and eye-tracking data. A total of 250 participants were assigned to either a feedback (treatment) or baseline condition and observed at three time points: the day of the experiment, then two weeks, and three months later. Participants played two types of games against a payoff-maximizing algorithm: single-stage games (3×3 normal-form games with a unique pure-strategy Nash equilibrium) and multi-stage games (a preliminary entry decision by the algorithm, followed — conditional on entry — by a simultaneous 2×2 coordination game). The treatment consisted of a learning phase in which participants played repeated single-stage games with feedback, whereas baseline participants received no feedback. This design allows us to study learning within context, persistence over time, and transfer of strategic sophistication from single- to multi-stage games.

Training generates large and persistent improvements in equilibrium choice rates in single-stage games. Treated subjects significantly outperform the baseline group at all follow-up horizons, with no evidence of decay over three months. Using eye-tracking data, we identify three attentional types — defined by characteristic patterns of information search — and show that behavioral gains arise across all of them. Alongside this, we identify a complementary mechanism: subjects initially focused on their own payoffs are significantly more likely to shift attention toward their opponent's payoffs over time, and this attentional restructuring predicts long-run improvements in equilibrium play.

We also document consistency in sophistication across environments: attentional types identified in single-stage games are correlated with performance in multi-stage games, with more sophisticated attention patterns associated with higher coordination rates. However, we find no evidence of transfer. Although performance improves over time in multi-stage games, treatment and baseline groups evolve in parallel, ruling out treatment-induced gains.

Overall, the results point to two distinct components of strategic learning—rule acquisition and attentional restructuring—and show that while strategic sophistication is durable and correlated with patterns of information acquisition across environments, its transfer remains limited.