Determining an individual’s strategic reasoning capability based solely on choice data is a complex task. This complexity arises because sophisticated players might have non-equilibrium beliefs about others, leading to non-equilibrium actions. In our study, we pair human participants with computer players known to be fully rational. This use of robot players allows us to disentangle limited reasoning capacity from belief formation and social biases. Our results show that, when paired with robots, subjects consistently demonstrate higher levels of rationality, compared to when paired with human players. Furthermore, players’ rationality levels are relatively stable across games when paired with robot players, even though those with intermediate rationality levels exhibit inconsistency across games. Leveraging our experimental design, we identify and document potential causes of this inconsistency.

We develop a new design for the experimental beauty-contest game (BCG) that is suitable for children in school age and test it with 114 schoolchildren aged 9–11 years as well as with adults. In addition, we collect a measure for cognitive skills to link these abilities with successful performance in the game. Results demonstrate that children can successfully understand and play a BCG. Choices start at a slightly higher level than those of adults but learning over time and depth of reasoning are largely comparable with the results of studies run with adults. Cognitive skills, measured as fluid IQ, are predictive only of whether children choose weakly dominated strategies but are neither associated with lower choices in the first round nor with successful performance in the BCG. In the implementation of our new design of the BCG with adults we find results largely in line with behavior in the classical BCG. Our new design for the experimental BCG allows to study the development of strategic interaction skills starting already in school age.

Experiments involving games have two dimensions of difficulty for subjects in the laboratory. One is understanding the rules and structure of the game and the other is forming beliefs about the behavior of other players. Typically, these two dimensions cannot be disentangled as belief formation crucially depends on the understanding of the game. We present the one-player guessing game, a variation of the two-player guessing game (Grosskopf and Nagel 2008), which turns an otherwise strategic game into an individual decision-making task. The results show that a majority of subjects fail to understand the structure of the game. Moreover, subjects with a better understanding of the structure of the game form more accurate beliefs of other player’s choices, and also better-respond to these beliefs.

The ability to strategically reason is important in many competitive environments. In this paper, we examine how relatively mild temporal variations in cognition affect reasoning in the Beauty Contest. The source of temporal cognition variation that we explore is the time-of-day that decisions are made. Our first result is that circadian mismatched subjects (i.e., those making decisions at off-peak time of day) display lower levels of strategic reasoning in the p < 1 Beauty Contest but not in the p > 1 game. This suggests that a cognitively more challenging environment is required for circadian mismatch to harm strategic reasoning. A second result is that choice adaptation or mimicry (i.e., a more automatic type of responding than what is typically considered to be “learning”) during repeated play is not significantly affected by circadian mismatch. This is consistent with the hypothesis that automatic thought is more resilient to cognitive resource depletion than controlled-thought decision making.