Neural correlates of depth of strategic reasoning in medial prefrontal cortex

Abstract

We used functional MRI (fMRI) to investigate human mental processes in a competitive interactive setting--the "beauty contest" game. This game is well-suited for investigating whether and how a player's mental processing incorporates the thinking process of others in strategic reasoning. We apply a cognitive hierarchy model to classify subject's choices in the experimental game according to the degree of strategic reasoning so that we can identify the neural substrates of different levels of strategizing. According to this model, high-level reasoners expect the others to behave strategically, whereas low-level reasoners choose based on the expectation that others will choose randomly. The data show that high-level reasoning and a measure of strategic IQ (related to winning in the game) correlate with the neural activity in the medial prefrontal cortex, demonstrating its crucial role in successful mentalizing. This supports a cognitive hierarchy model of human brain and behavior.

Fig. 1.

(A) Rules of the basic game and conditions. The figure shows the computer screen for each experimental condition. The participants were asked to choose a number between 0 and 100. The winner got 10 euros (or an equal share with those who tie) and is the person whose number is closest to the target [a parameter multiplier (here 2/3) times the average of 10 numbers]. The 10 numbers are the choices of either 10 human participants (human condition) or of one participant and a computer program who chooses uniform randomly 9 numbers from 0 to100 (computer condition). The losers got nothing. All this is known to the participants. There were 13 different parameter multipliers. Each multiplier was presented once in each condition in a pseudorandom order. In a control condition (random condition) the participants were asked to pronounce a random number between 0 and 100. In the calculation task (session 2) subjects were asked to calculate the product between one (C1 condition) or 2 factors (C2 condition) times a number, and additionally a random condition. (B) Game theoretic prediction (for M = 2/3): If all participants are rational and know that everybody else is rational and so on (common knowledge of rationality) then everybody should choose 0, because no one should choose >100*2/3 = 66 (weakly dominated choices); thus all numbers in E (0) are eliminated. In the reduced game nobody should choose >100*(2/3)² = 44, thus eliminating E (1), and so on until 0 is reached. If M > 1 then all players choosing 100 also represents an equilibrium. (C) Bounded rational model. Cognitive hierarchy (for M = 2/3) is a cognitively and descriptively more plausible model (17). A random player level 0 [L (0)] chooses uniformly from 0 to 100 with an average of 50. A best reply to this is 50*2/3 = 33 (level 1). If everybody chooses 33 then best reply is 50*(2/3)² = 22 (level 2), etc. A subject is strategic of degree k if he chooses the number 50*M^k, called level k.

Fig. 2.

Patterns of behavior and brain activity for low and high levels of reasoning. (A) Behavioral results. Here, we present the 26 choices of 2 representative participants for each parameter value M in the human (blue dots) and computer (triangles) conditions, separately. (Left) the choices of one participant representing a so-called low-level type. In both the computer condition (triangles) and the human condition (blue dots) he chose near the theoretical (Cognitive Hierarchy Model) level 1 line (brown line with choices equal to 50*M). (Right) the choices of one high-level type participant. In the computer condition he chose near the theoretical level 1 line. In the human condition he chose near the theoretical level 2 line (blue line with choices equal to 50*M²). (Below) We plot the choice of the 2 participants for the computer and human conditions for M = 2/3. In total we classified 10 participants as level 1 (low level) and 7 as greater than level 1 (high level). Three participants played in a random manner. (B) fMRI results. Choosing a number in the human condition in contrast to the computer condition was associated with relative enhanced activity in the rostral anterior cingulate cortex (Left) Low level of reasoning subjects, random effect analysis n = 10 (rACC, MNI coordinates: x = −9, y = 36, z = 3); and (Right) high level of reasoning subjects, random effect analysis n = 7 activity in the dorsal portion of the medial prefrontal cortex (mPFC, MNI coordinates: x = 3, y = 48, z = 24) and ventral mPFC (relatively less deactivated, MNI coordinates: x = 3, y = 51, z = −9). Group data thresholded at P < 0.001, uncorrected, is plotted on sagittal sections of a normalized canonical template brain.

Fig. 3.

Strategic IQ and medial prefrontal cortex. Activity in the dorsal portion of the medial prefrontal cortex related to play against human opponents (mPFC, MNI coordinates x = 0, y = 48, z = 24; the mean parameter estimates for each participant were extracted from the functional ROI obtained from the random effect analysis human vs. computer, n = 20) was correlated with a measure of strategic IQ (the quadratic distance of choices to the winning numbers using a recombinant estimation method). Values closer to 0 indicate higher strategic IQ. Note: red dots and blue dots indicate high and low level of reasoning participants, respectively; participants who played in a random manner are excluded from the figure.