The determinants of response time in a repeated constant-sum game: A robust Bayesian hierarchical dual-process model

The investigation of response time and behavior has a long tradition in cognitive psychology, particularly for non-strategic decision-making. Recently, experimental economists have also studied response time in strategic interactions, but with an emphasis on either one-shot games or repeated social-dilemmas. I investigate the determinants of response time in a repeated (pure-conflict) game, admitting a unique mixed strategy Nash equilibrium, with fixed partner matching. Response times depend upon the interaction of two decision models embedded in a dual-process framework (Achtziger and Alós-Ferrer, 2014; Alós-Ferrer, 2016). The first decision model is the commonly used win-stay/lose-shift heuristic and the second the pattern-detecting reinforcement learning model in Spiliopoulos (2013b). The former is less complex and can be executed more quickly than the latter. As predicted, conflict between these two models (i.e., each one recommending a different course of action) led to longer response times than cases without conflict. The dual-process framework makes other qualitative response time predictions arising from the interaction between the existence (or not) of conflict and which one of the two decision models the chosen action is consistent with-these were broadly verified by the data. Other determinants of RT were hypothesized on the basis of existing theory and tested empirically. Response times were strongly dependent on the actions chosen by both players in the previous rounds and the resulting outcomes. Specifically, response time was shortest after a win in the previous round where the maximum possible payoff was obtained; response time after losses was significantly longer. Strongly auto-correlated behavior (regardless of its sign) was also associated with longer response times. I conclude that, similar to other tasks, there is a strong coupling in repeated games between behavior and RT, which can be exploited to further our understanding of decision making.