The computation of strategic learning in repeated social competitive interactions: Learning sophistication, reward attractor points and strategic asymmetry

Social interactions rely on our ability to learn and adjust our behavior to the behavior of others. Strategic games provide a useful framework to study the cognitive processes involved in the formation of beliefs about the others’ intentions and behavior, what we may call strategic theory of mind. Through the years, the growing field of behavioral economics provided evidence of a systematic departure of human’s behavior from the optimal game theoretical prescriptions. One hypothesis posits that human’s ability to accurately process the other’s behavior is somehow bounded. The question of what constraints the formation of sufficiently high order beliefs remained unanswered. We hypothesize that maximizing final earnings in a competitive repeated game setting, requires moving away from reward-based learning to engage in sophisticated belief-based learning. Overcoming the attraction of the immediate rewards by displaying a computationally costly type of learning might not be a strategy shared among all individuals. In this work, we manipulated the reward structure of the interaction so that the action displayed by the two types of learning becomes (respectively not) discriminable, giving a relative strategic (resp. dis) advantage to the participant given the role endorsed during the interaction. We employed a computational modeling approach to characterize the individual level of belief learning sophistication in three types of interactions (agent-agent, human-human and human-agent). The analysis of the participants’ choice behavior revealed that the strategic learning level drives the formation of more accurate beliefs and eventually leads to convergence towards game optimality (equilibrium). More specifically we show that the game structure interacts with the level of engagement in strategically sophisticated learning to explain the outcome of the interaction. This study provides the first evidence of a key implication of strategic learning heterogeneity in equilibrium departure and provides insight to explain the emergence of a leader-follower dynamics of choice. AUTHOR SUMMARY Dynamic interaction between individuals appears to be a cornerstone for understanding how humans grasp other minds. During a strategic interaction, in which the outcome of one’s action depends directly on what the other individual decides, it appears crucial to anticipate the other’s actions in order to adjust our own behavior. In theory, choosing optimally in a strategic setting requires that both players hold correct beliefs over their opponent’s behavior and best-respond to it. However, in practice humans systematically deviate from the game-theoretical (equilibrium), suggesting that our ability to form accurate beliefs is cognitively and/or contextually constrained. Previous studies using computational modelling suggested that during a repeated game interaction humans vary in the sophistication of their learning process leading to the formation of beliefs over their opponent’s behavior of different orders of complexity (level of recursive thinking such as “I think that you think that …”). In this work we show that the individual engagement in sophisticated (belief-based) learning drives the convergence towards equilibrium and ultimately performance. Moreover, we show that this effect is influenced by both the game environment and the cognitive capacity of the participants, shaping the very dynamic of the social interaction. DATA AVAILABILITY The authors confirm that upon publication the raw behavioral data and Matlab code for reconstruction of all figures, computational models and statistical analyses will be made available for download at the following URL: https://zenodo.org/