Abstract
Dualprocess theories distinguish between intuition (fast and emotional) and reasoning (slow and controlled) as a basis for human decisionmaking. We contrast dominancesolvable games, which can be solved by stepbystep deliberative reasoning, with pure coordination games, which must be solved intuitively. Using functional magnetic resonance imaging, we found that the middle frontal gyrus, the inferior parietal lobule, and the precuneus were more active in dominancesolvable games than in coordination games. The insula and anterior cingulate cortex showed the opposite pattern. Moreover, precuneus activity correlates positively with how “effortful” a dominancesolvable game is, whereas insula activity correlates positively with how “effortless” a coordination game is.
There are games in which, given sufficient computational capacity, each player can determine an optimal strategy using only the mathematical structure of the game. Checkers is a typical example; if each player plays optimally, then checkers must end in a draw (1). There are other games, though, in which players are required to coordinate their actions, and this requires a “meeting of the minds” that is not amenable to mathematical analysis. In this study, we contrast dominancesolvable games, where finding an optimal strategy is purely a mathematical problem, with pure coordination games, where successful play requires the players to go beyond the mathematics of the game (2).
A strategy is “dominated” if it is always worse than another strategy. Rational players eliminate all dominated strategies from consideration, creating a new game with fewer strategies, some of which may again be dominated. If this process can be iterated until a unique strategy remains for each player, then the game is dominancesolvable. Implementing this gametheoretic textbook procedure of stepbystep deliberation would likely require neural structures underlying cognitive processing, reasoning, and memory maintenance.
In a pure coordination game, each player’s objective is simply to match the action of the other player (without communicating) (3). In “Nash equilibrium,” both players choose the same action, but it is not possible to determine mathematically which action to choose, that is, on which Nash equilibrium to coordinate. In (4), participants were asked to name (among other things) a color, a number, and a year. When rewards did not depend on their answers, blue and red were about equally popular colors; the most popular numbers were 7, 2, and 10; and only 6.8% named the current year. However, when the game was turned into a pure coordination game, by rewarding those who matched the choices of others, red became by far the most frequent color, 1 the most frequent number, and 61.1% named the current year. Red, 1, and the current year had become “focal points,” objects with “symbolic or connotative characteristics that transcend the mathematical structure of the game” (5). Automatic (fast, effortless) recognition of salient characteristics of complex highdimensional objects is typical of intuitive judgments (6). Focal points must have properties that each participant recognizes as being salient not only to herself but also to others, but this too may be at least partly an intuitive judgment, using salience to oneself as an input. In general, intuition and deliberative reasoning are mental processes with very different properties. Intuition is fast, automatic, emotional, and effortless. Reasoning is slow, rulegoverned, controlled, and effortful (7).
We designed two kinds of games, number games and box games. A dominancesolvable number game is shown at the top of Fig. 1A. Two players, X (“you”) and Y (“other”), simultaneously pick a number from 0, 1, 2, or 3, without communicating. Each player’s objective is to be as close as possible to a “target number.” The instruction “other: you” means Y’s target is “the number chosen by X,” so Y wants to match X’s choice. The instruction “you: other+1” means X’s target is “one plus the number chosen by Y.” A player who achieves her objective receives a reward [supporting online material (SOM), S1.2]. For example, if X chooses 1 and Y chooses 0, then only X is rewarded. Because X’s target is at least 1, choosing 0 is dominated for X and should be eliminated. This makes 0 dominated for Y, who wants to match X’s choice. Eliminating 0 for Y makes X’s target at least 2, so eliminates 1 for X. Three more steps lead to the formal gametheoretic solution: Each player chooses 3 (SOM, S1.3). To obtain a pure coordination game, we modify the rules slightly to make each player’s target the other player’s chosen number (Fig. 1A, bottom). In the new game, there is no formal gametheoretic reason to choose one number over another.
A dominancesolvable box game is displayed at the top of Fig. 1B. Two players, X (“you”) and Y (“other”), simultaneously choose a box in a 3 by 3 matrix by picking a letter indicating row A, B, or C and a number indicating column 1, 2, or 3. For example, A3 is the box in the northeast corner of the matrix. The instruction “you: 1R” means X’s target is “the box to the right of Y’s choice.” Similarly, the instruction “other: 1R 1U” means Y’s target is “the box to the right of and above player X’s choice” (SOM, S1.2). For example, if X chooses B1 and Y chooses A2, then only Y gets a reward. The gametheoretic solution is A3 for each player (SOM, S1.3). To obtain a pure coordination game, we make each player’s target the box chosen by the other player (Fig. 1B, bottom).
Using functional magnetic resonance imaging (fMRI), we scanned 21 participants when they played games against a pool of students (SOM, S1). We used two experimental treatments: number game and box game. Each treatment had two conditions: dominancesolvable and pure coordination. All games were slight variations of the games shown in Fig. 1 (table S1). Each participant played 40 dominancesolvable and 40 pure coordination games. Response times were significantly faster in coordination games than in dominancesolvable games, consistent with the idea that intuitive decisions are faster than stepbystep deliberations (8) (SOM, S2.7). The games were displayed using the intuitive graphics of Fig. 1, which we hoped would help the comprehension of the games. The behavioral results are consistent with this (SOM, S2). In dominancesolvable games, our participants picked the gametheoretic solution 79.26% of the time. In coordination games, when participants’ choices were paired with the modal responses from the pool of students, coordination was achieved 69.92% of the time. When randomly paired with a pool student, participants chose the “best response” (the strategy which yielded a reward) in 66.97% of the dominancesolvable games and in 46.10% of the pure coordination games. If choice had been completely random, participants would have earned rewards in only 21.24% of the dominancesolvable games and in only 18.66% of the pure coordination games. The P value of Pearson’s chisquare test on whether participants’ choices were uniformly random is 0.00 for both dominancesolvable and pure coordination games. Previous experiments have suggested that players do not complete more than two or three steps of iterated elimination of dominated strategies (9). Our participants did better, perhaps due to the intuitive displays. The impressive feats of tacit coordination are consistent with (4).
Comparing dominancesolvable games with coordination games, higher activation was found bilaterally in the frontal and parietal regions. In the frontal cortex, the most prominent area of activation lies in the middle frontal gyrus, extending upward to the superior frontal gyrus. In the parietal cortex, activation was observed in precuneus and inferior parietal lobule. In the left inferior parietal activation, it reaches downward to the angular gyrus (Fig. 2 and table S2). Previous studies found frontoparietal activity when tasks required attention, conscious perception, reasoning, or memorizing (10). For instance, frontoparietal activation is observed when contrasting logical reasoning with tasks in which reasoning is not required (11), contrasting challenging reasoning tasks with straightforward ones (12), or contrasting a meaningful middle game position with a random game position in chess (13). The higher frontoparietal activation in dominancesolvable games squares well with these previous studies, because the textbook solution procedure requires a sequence of reasoning steps. In each step, the player eliminates dominated strategies, holds remaining strategies in mind, and then iterates.
Working memory is crucial for problem solving, reasoning, and planning (14, 15). It allows the temporary retention and manipulation of information in a system of limited capacity (16). The working memory model contains a central executive system for control and two subsystems for maintaining verbal and visuospatial information. Frontoparietal activation in dominancesolvable games can be interpreted according to this model. First, the participant must verbally encode and hold in mind the targets of both players (17). The inferior parietal lobule has been implicated in verbal memory storage and may serve this purpose (18, 19). Eliminating dominated strategies presumably engages the central executive, which is hypothesized to manipulate the contents of storage. The activation of the middle frontal gyrus may relate to this, as it is thought to execute goaldirected operations (18, 20, 21). Posterior parietal cortex plays a role in visuospatial working memory (18, 21). The precuneus, the medial portion of the posterior parietal cortex, may be related to imagery (mental representations of objects that are not perceptually present) and memory retrieval (22–25). Keeping track of eliminated strategies may require generating and keeping in mind a mental image which must be retrieved in each step of elimination. We caution that the iterated elimination is a complex algorithm, and neatly mapping it onto the working memory model is speculative. Also, some participants may have deviated from the algorithm. However, working memory may still have been important. Postscan interviews strongly suggested that the participants used deliberative mathematical reasoning in dominancesolvable games (SOM, S6). Most explicitly stated that they would keep in mind both targets, going back and forth, and eliminating strategies.
Among the areas showing greater activation for coordination games than for dominancesolvable games were bilateral insulae and anterior cingulate cortex (ACC) (Fig. 3 and table S3). The activation in the insular cortex lies in the middle insula, extending mostly toward the posterior insula. In the cingulate, the activation extends from the caudal ACC to the cingulate motor area (CMA) and the supplementary motor area (SMA). The insula has previously been implicated in subjective prereflective and reflective representations of ongoing changes in internal bodily and feeling states (26). The ACC seems to act as a conflict monitor when tasks require attention, novel or openended responses, or when cognitive uncertainty exists (27). These areas are also activated in many paradigms with strong social content or emotions, such as when participants contemplate cooperating instead of competing with another person (28), when they judge other persons to be trustworthy instead of being untrustworthy (29), or when they experience social emotions such as empathy (30) or love (31). These emotions might have evolved to ensure quick response to the factors arousing them in the presence of many stimuli. Many social interactions involve myriad stimuli but demand immediate decisions. Rapid processing and extraction of the most salient aspects of complex situations is characteristic of intuitive decisionmaking. Deciding within the context of a coordination game which Nash equilibrium has the most salient characteristics requires rapid processing of various cultural connotations as well as geometric symmetry, centrality or even mathematical oddity (SOM, S7.2). The insula and ACC might be part of a general network contributing to a quick and flexible evaluation of complex multidimensional experiences, and this may be the common denominator between our coordination games and the earlier experiments on social decisionmaking (32).
The key to coordination may be the ability to make judgments of salience common to both. That is, the participant must identify features that are likely to be salient not only to herself but also to the pool student. Nevertheless, mentally simulating the pool student’s judgment of salience may require the participant to use her own intuitive judgment of salience as an input. A model suggests that the middle insula receives inputs about the physiological condition of the body from the posterior insula and integrates this with salient environmental stimuli (33). It has also been suggested that insula and ACC are a part of a general network that responds to varied forms of personal salience (34). For instance, the posterior insula and the SMA/CMA are shown to be responsive to changes of many sensory modalities (35), whereas the anterior insula and ACC are sensitive to novelty (36). A study using singlecell recording in the caudal ACC indicates that neurons in caudal ACC respond differentially to highconflict and lowconflict tasks (37). These studies all point to a possible role of insula and ACC in identifying salience and provide support for the hypothesis that the higher activation we observe is due to participants extracting salient features in order to coordinate. A recent study of functional connectivity between the insula and the cingulate also agrees with our finding (38).
The textbook procedure for dominancesolvable games requires a welldefined number of steps (SOM, S2.3). If participants use this procedure, then the activation of the frontoparietal network might correlate with the required number of steps. For coordination games, the normalized coordination index (NCI) measures how well coordination is achieved (39) (SOM, S2.5). A high NCI may reflect the existence of an obvious focal point. If activation of the insula or ACC reflects the “gut feeling” aroused by a salient focal point, then it might correlate with the NCI. To investigate these hypotheses at the trialbytrial level, a second model was built. We divided the 40 dominancesolvable games into 20 “hard” and 20 “easy” games, depending on the number of steps required. Similarly, 20 coordination games with high NCI were classified as “highly focal,” and 20 games with low NCI were “less focal.” In the 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 dominancesolvable 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 memoryrelated imagery and memory retrieval may explain the greater precuneus activation in hard dominancesolvable 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 dominancesolvable 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 dominancesolvable games (Fig. 4C and table S12), which suggests that dominancesolvable 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 dominancesolvable games were harder. The “fast and effortless” process was more strongly activated when coordination was easy.
Supporting Online Material
www.sciencemag.org/cgi/content/full/324/5926/519/DC1
Materials and Methods
Figs. S1 to S9
Tables S1 to S18
References

↵* These authors contributed equally to this work.
References and Notes
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 ↵ Previous fMRI studies of gameplaying include Gallagher et al. (43) and Bhatt and Camerer (44), but they address different issues. In particular, Bhatt and Camerer found higher insula and ACC activity when comparing choices to firstorder beliefs in dominancesolvable games.
 ↵ We are considering here coordination without visual or other contact. Nonhuman primates seem able to coordinate their actions (simultaneously pulling on bars to obtain food) when they are in visual contact (45).
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 ↵ See (46). In our experiment, the average number of steps required to find out the gametheoretic solution for all 40 dominancesolvable games is 3.675.
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 ↵ In coordination games, the participant has to encode and hold this information as well. However, because the targets of both players are the same, the demand on this capacity should be smaller.
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 ↵ See (47). The NCI can be interpreted as the probability that two randomly chosen individuals make the same choice relative to the probability of successful coordination if all choose randomly (SOM, S2.5).
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 We thank M. Hsu for helpful comments on the manuscript and J.Y. Leu, J.T.Y. Wang, D. Niddam, and participants at many seminars for discussions. Technical assistance from C.R. Chou, C.T. Chen, C.H. Lan, S.C. Lin, K.L. Chen, Y.Y. Chung, W.Y. Lin, S. Hsu, R. Chen, and the National Taiwan University Hospital MRI Laboratory is greatly appreciated. This work was supported by the National Science Council of Taiwan (grant NSC 942415H002004).