Cognitive Sophistication and Response Times

Cognitive capacities differ among individuals. Experimentally observed behavior often shows significant inter-individual differences in decision making, and this observation has given rise to a rich literature developing theories endowing individuals with different levels of strategic sophistication or reasoning capability. Such models of iterative thinking (Stahl 1993; Stahl and Wilson 1995; Ho et al. 1998) are built on the idea that heterogeneity in depth of reasoning is the source of differences in observed behavior. They usually start by postulating a specific behavior of non-strategic types (often assumed to be random, or based on salience), and assume that higher types best-respond to the behavior of lower types, thus associating different responses with different “levels of strategic sophistication.” Following this approach, a large body of experimental literature has used observed choices to classify individuals in different cognitive-reasoning categories or “levels.” This way, choice data is used to make inferences regarding the process that lead to a particular choice. The problem with this approach is that the same choice is always attributed to the same level, although it might very well be the result of completely different decision rules. Choice data alone is not sufficient to distinguish such cases and, hence, additional data is necessary to make better inferences regarding the underlying processes. There is a growing literature (Coricelli and Nagel 2009; Brañas-Garza et al. 2012) employing other sources of evidence suggesting that individuals follow step-wise reasoning processes. Those works show that reasoning in the beauty contest game (Nagel 1995), which is the workhorse in the literature on iterative thinking, correlates with neural activity in areas of the brain associated with mentalizing (Theory of Mind network) and relate higher cognitive ability (as measured, e.g., by the Cognitive Reflection Test) with more steps of reasoning. Recently, Alaoui and Penta (2016) have incorporated response times into a model of endogenous depth of reasoning, with the key assumption being that each additional step of reasoning increases response times. In this article we measure response times in a series of games that involve iterative thinking. In our experiment subjects play a one-shot beauty contest game and a series of variations of the 11-20 money request game (Arad and Rubinstein 2012). More precisely, we use different variants of a graphical version of the 11-20 game (Goeree et al. forthcoming), which allows to vary the payoff structure without affecting the underlying best-reply structure. The idea is to use response times as a proxy for cognitive effort, or deliberation, in these strategic situations. We argue that additional evidence in the form of process data such as response times can be used to investigate whether step-wise reasoning is actually the procedure underlying behavior in these games. As a first result, we find longer response times for higher guesses in the beauty contest game (commonly associated with more steps of reasoning), which we interpret as additional evidence that higher-level choices indeed require more deliberation. Second, we show that also in the 1120 game longer response times are correlated with higher-level choices in situations where the payoff structure is such that following level-k type of reasoning is salient enough. However, this relation breaks down when there is a conflict with alternative decision rules (e.g., based on the