second model, the two main conditions were parametrically modulated by the two categories, respectively (SOM, S5.1). The activation of the precuneus was higher for hard dominance-solvable games than for easy ones ( Fig. 4A and table S10). The activation of the insula was higher for the highly focal coordination games than for less focal ones ( Fig. 4B and table S11). Previous studies also found that precuneus activity increased when the number of planned moves increased (40, 41). The higher demand for memory-related imagery and memory retrieval may explain the greater precuneus activation in hard dominance-solvable games. In highly focal coordination games, the participants may have felt quite strongly that the pool students must notice the same salient feature. This may explain why insula activation correlates with NCI.Participants might have disagreed about which games were difficult. We built a third model to investigate whether the frontoparietal activation correlates with how hard a dominance-solvable game is and whether the activation in insula and ACC correlates with how easy a coordination game is. Here, the two main conditions were parametrically modulated by each participant's probability of obtaining a reward in each game (SOM, S2.2 and S5.2). We found a negative correlation between the activation of the precuneus and the participant's probability of obtaining a reward in dominance-solvable games ( Fig. 4C and table S12), which suggests that dominance-solvable games that yielded lower payoffs presented harder mental challenges. In a previous study on working memory, precuneus activity positively correlated with response times, a measure of mental effort (24). Both findings are consistent with the interpretation that subjective measures reflecting harder tasks (higher efforts) correlate with activation in precuneus. A positive correlation between insula activation and the participant's probability of obtaining a reward again suggests that coordination games with a highly salient feature strongly activated the "gut feeling" reported by many participants (Fig. 4D and table S13). A previous study found that the subjective rating of "chills intensity" in music correlates with activation of insula (42). Both findings are consistent with the interpretation that the subjective intensity of how salient a stimulus is correlates with activation in insula.As mentioned, choices were made significantly faster in coordination games than in dominancesolvable games. The results of the second and third models provide additional support for the idea that intuitive and deliberative mental processes have quite different properties. The "slow and effortful" process was more heavily taxed when the dominance-solvable games were harder. The "fast and effortless" process was more strongly activated when coordination was easy.

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