Cognitive Load and Strategic Sophistication

Allred, Sarah; Duffy, Sean; Smith, John · 2013 · Crossref

DOI: 10.2139/ssrn.2289342

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Summary

This paper investigates the relationship between cognitive load and strategic sophistication in game theory contexts. The authors address a key limitation in existing literature: studies correlating measured cognitive ability with strategic behavior cannot rule out the possibility that unobserved traits, rather than cognitive ability itself, drive strategic differences. To isolate the causal effect of cognitive resources, Allred, Duffy, and Smith employ a within-subject experimental design where they manipulate the cognitive load placed on subjects’ working memory. By observing the same individuals under both high and low cognitive loads, the study aims to determine whether reduced cognitive resources uniformly decrease strategic sophistication or produce more complex behavioral patterns. The experiment involved 164 subjects who played a series of one-shot games, including ten 3x3 matrix games, a simplified 1-10 game (a variant of the 11-20 game), and a beauty contest game. Before each game, subjects were required to memorize a binary number string. In the low-load condition, subjects memorized a three-digit string; in the high-load condition, they memorized a nine-digit string. This manipulation was designed to occupy working memory capacity, thereby reducing the resources available for deliberative thought. The study used a within-subject design with alternating loads to control for individual differences and potential payment biases associated with between-subject designs. Subjects also reported their beliefs about opponents’ actions in the 3x3 games. The results reveal a nuanced and nonmonotonic relationship between cognitive load and strategic sophistication, driven by two competing effects. First, high cognitive load impairs the ability to compute optimal decisions. Second, subjects under high load perceive themselves as cognitively disadvantaged relative to their opponents, leading them to anticipate more sophisticated play from others. In the relatively simple 1-10 game, the second effect dominated: high-load subjects chose lower numbers, indicating more strategic behavior consistent with expecting opponents to play strategically. Conversely, in the more complex beauty contest game, the first effect dominated: high-load subjects chose higher numbers, indicating less strategic behavior due to computational difficulties. In the 3x3 games, high-load subjects were less sensitive to their own dominated strategies but more sensitive to their opponents’ dominated strategies, further supporting the dual-effect hypothesis. The significance of these findings lies in challenging the assumption that lower cognitive ability or resources always lead to less sophisticated strategic behavior. The study suggests that the impact of cognitive constraints depends on the strategic setting’s complexity. When computational demands are low, awareness of one’s own cognitive disadvantage can enhance strategic reasoning by adjusting beliefs about opponents. However, when computational demands are high, the inability to process information reduces strategic sophistication. This provides indirect evidence for the literature on cognitive ability and strategic behavior, highlighting the importance of distinguishing between computational capacity and belief formation in models of bounded rationality.

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• mental demand