The Measurement and Neural Foundations

Collaborative Research on

The Measurement and Neural Foundationsof Strategic IQ

1. Introduction

We propose to create a system to measure how well different people reason in social (game-theoretic) situations, where the choices of other people (or organizations, including companies and nation-states) affect their own outcomes and choices unfold over time. Understanding these situations helps us understand human social dynamics and enhance human performance.

The work is interdisciplinary, bringing together strands of mathematical game theory, psychology, and neurobiology, in order to create a measure of “strategic IQ”for calibrating how well people with different skills think strategically. This proposal combines our expertise in experimental studies of strategic thinking with access to special subject populations with localized brain legions, experienced business executives, and technologies for brain imaging.

The concept of strategic IQ can have scientific value because these data, along with neuroscience data, can also be used to understand the psychological and neural foundations of strategic thinking. A strategic IQ measure also has practical value: To help people evaluate their own skills, to aid in personnel selection (e.g., screening corporate strategists, diplomats, or military personnel), and to show people where their strategic thinking can be improved. Understanding the neural foundations of strategic thinking can also help with diagnosis and rehabilitation of disorders, and for immunizing elderly populations from potential risks (since prefrontal and hippocampal regions, which we focus on, decline most rapidly with age) in elderly populations.

Our research starts with game theory. Game theory has proved enormously useful in economics, among social sciences, and can potentially unify diverse disciplines by providing a common language. Game theory provides a way to define strategic situations mathematically—viz., in terms of players, their information and strategies, an order of moves, and how players evaluate consequences which result from all the strategy choices. Most analyses of how people actually behave in games use some concept of equilibrium (i.e., players accurately guess by learning or introspection what others will do). While the concept of equilibrium is useful as an idealized model, hundreds of experiments with many groups of people (including subjects who are highly financially-motivated and trained in game theory) show that actual behaviors are often inconsistent with the equilibrium assumption (Camerer, 2003).

The fact that people do not always make equilibrium choices implies that there may be reliable, measurable differences in the ability of people to think strategically, which we call strategic IQ. Strategic IQ measures a person's ability to guess accurately what others will do in situations where two or more parties do not have prior contractual agreements (agreeing on a contract may be the strategic situation of interest), each party can choose several possible courses of action, and each individual payoff depends on his or her actions, the actions of the other parties, and on chance events. Examples include war, international trade negotiation, rivalry between firms to gain market share, and child custody fights between divorced couples.

A person's strategic IQ is her total normalized payoff when playing with others in a series of carefully designed competitive situations. Note that IQ is dynamic-- a person's IQ can increase or decrease as a result of others changing their choices, and can be improved by sharpening a person's understanding of typical behavior. A premise of the engineering applications of our approach is that people differ in their IQ-- this variation enables us to understand the neural foundations of strategic thinking-- and that it is possible to improve IQ by training.

We propose to measure strategic IQ by how much people earn in a battery of games, when playing against the previous choices of a population of specified players. Measures of strategic IQ's will be compared to three benchmarks-- equilibrium choices from game theory analyses; a “clairvoyant” best guess about what others do (based on the data we collect), which by definition an upper bound on strategic IQ; and a “cognitive hierarchy” model developed in previously-supported NSF research.

As noted, an important use of strategic IQ is basic scientific research. To this end, we will give the battery of games to five specially-selected populations: (i) Undergraduates who are superbly skilled in mathematics (screened groups of Berkeley and Caltech students); (ii) undergraduate and graduate students specially trained in game theory[1]; (iii) chess players recruited at tournaments (since their numerical chess-skill ratings can be compared to their strategic IQ’s); (iv) highly-experienced business managers (available through executive education activities at Berkeley where PI Ho teaches); and (v) patients with specialized brain lesions (available through the University of Iowa’s unique Cognitive Neuroscience Patient Registry, which PI Adolphs has used extensively).Other interesting subject pools will be sampled as opportunities arise.

Evidence about what games the lesion patients play poorly will help diagnose which brain circuitry is used in various types of strategic thinking. These data are complements to planned fMRI imaging: Imaging is useful for seeing all the parts of neural circuitry (while lesion patient deficits show the “necessary” parts); and lesion patients are useful for studying parts of the brain that are not easily imaged (especially insula and orbitofrontal cortex), or where delicate designs are needed. This part of the project also contributes to basic neuroscience by providing a new set of tasks which can help refine our understanding of the functions of higher-order cognition in prefrontal cortex, which is not thoroughly understood (e.g., Wood and Grafman, 2003).

Before we continue, it is important to note that strategizing is not merely outfoxing opponents in “zero-sum” games, where one player loses if another player wins. Strategic thinking generally refers to guessing correctly what others are likely to do. Therefore, strategic thinking can often be mutually beneficial, in games where more strategic thinking by both players can help them achieve joint gains. So raising one person’s strategic IQ may help others.

Also, the term “IQ'” just denotes a numerical measure of how well different people perform in a specific test. We hope to avoid debates about whether there is such a thing as general intelligence, or whether such tests are inherently biased or used for socially harmful purposes. The strategic IQ measures simply starts to put an important skill on a scientific basis, which may also have some practical use. Our approach follows Gardner (1983) and others who distinguish “multiple intelligences” (cf. Salovey, Mayer and Caruso, 2002 on “emotional intelligence”). Gardner's seven types of intelligence include logic/mathematical reasoning and interpersonal intelligence. Strategic IQ is a combination of these two subtypes.

2. Proposed Activities

a. Strategic IQ measurement: First we will develop a battery of games and a database of how various groups play those games under conditions which are typical in experimental economics-- namely, the game is described abstractly and subjects earn payoffs which depend on their choices and the choices of others whom they are paired with.

b. Creating theoretical benchmarks: It is useful to compare human performance on these games with two theoretic benchmarks-- the game-theoretic advice from equilibrium models, and a simple descriptive model based on “cognitive hierarchy” (CH) models of naturally-limited cognition (extending earlier work by PI Camerer and Ho). Doing this comparison requires extending the CH models to dynamic “extensive form” games, which is a basic scientific contribution.

c. Studying specially-selected groups: Experiments with lesion patients from the Iowa database will show which neural regions are important in the various components of strategic thinking identified in Table 1. Other experiments with specialized populations, including experts and others will tell us more about likely regions used in different kinds of strategic thinking.

d. Imaging neural activity: fMRI imaging and tracking of eye movements with typical subjects will supplement what we learn from (3) about neural regions active in strategic thinking. Imaging will be done at Caltech's BroadImagingCenter where PI Camerer has been active (e.g., Tomlin et al, 2004) and there is good access to scanner time. The fMRI scanner goggles worn by subjects also include tiny cameras so the eye movements of subjects can be measured while they are in the scanner (see Camerer et al, 1994, for an early application of eye-tracking to game theory).

3. Strategic IQ measurement

To illustrate the skeleton of a strategic IQ measure, we will discuss five classes of games which we hypothesize to tap different dimensions of strategic IQ.We illustrate each class with only one exemplar game, but in practice we will use many games with similar strategic properties (some of which are enumerated in footnotes annotating the section that describes each exemplar game).

Standard psychometric methods like factor analysis will be used to see which components of strategic IQ congeal statistically. That is, each game will be treated as a separate test item, and we will evaluate statistically which test items correlate into distinct factors. Assume there are J dimensions altogether and each dimension j has K(j) test questions (i.e., games). If N people take the test,each participant i's strategic IQ(i) is determined as follows: Eachindividual will have N-1 possible matches in each of the competitive situations. The total payoffsfor player i will be i = j=1J k=1K(j) m=1N-1 i(j,k,m), where i(j,k,m) is player i’s payoff from test question k in dimension j, in each match m with one of the N-1 other players. The payoffs will be scaled so each item receives equal weight. Strategic IQ(i) is then normalized by subtracting the mean and dividing by the variance.

Of course, the items may cluster into categories which are different than the five we hypothesize. The simple psychometrics is important because most recent mathematical models in behavioral game theory assume that players have distinct emotional or cognitive “types” which will lead to correlated behavior across games, but little is known about how reliable types are across a wide range of games. Psychometric testing of which components of game performance are correlated will reveal whether there are separate dimensions of strategic thinking-- for example, whether anticipating how others will react emotionally to outcomes which give different payoffs to different players is correlated with planning ahead in dynamic games. We will also compare strategic IQ measures to a measures of general intelligence from a short-form of the Wechsler scale (Satz and Mogel,1962) and a measure of emotional intelligence (MSCEIT, e.g. Lopes et al, in press).

Analyses with lesion patients who have localized brain damage, and expert subgroups (e.g., the undergraduate chess players), and fMRI measures of brain activity on typical normal control

Figure 1: Photographs of the human brain schematizing some of the anatomical regions we are exploring. Color-coded regions are shown on lateral (A and B) and medial (middle, C) views of a human brain.

1. The insula (purple), can only be revealed by dissection of the overlying frontal cortex. It is buried underneath the frontal lobe.
2. Sectors of prefrontal cortex we will investigate include a cytoarchitectonic region, Brodmann’s area 10 (frontal polar cortex, orange), as well as more general anatomical regions that encompass several cytoarchitectonic regions: dorsolateral prefrontal cortex (blue) and ventromedial (VM) prefrontal cortex (green). The hippocampal formation is buried within the medial temporal lobe; its outline projected onto the lateral surface is indicated in red.
3. Visible on the medial surface are the ventromedial prefrontal cortex (green) and anterior cingulate cortex (yellow).

subjects, enable us to potentially link performance on different item-clusters to distinct neural regions which underly components of strategic thinking. This analysis may also provide new ways to categorize brain function which might interest neuroscientists.

These games have all been well-studied experimentally (see Camerer, 2003). In fact, the large amount of experimentaldata from previous studies are what permit the construction of a reliable IQ measure (since it calibrates a person’s choices against a large amount of historical play).

Each section below describes one component of strategic thinking, an exemplar game which illustrates the strategic thinking component, some hypothesized psychological processes, and tentative candidate brain regions that can be explored as neural loci of the psychological process. Table 1 summarizes this exploratory structure. Note that very little is known about the brain circuitry that creates these processes— indeed, a major contribution of our proposed research is to learn more-- so the hypothesized brain processes are tentative and the work will be exploratory. Figure 1 shows views of the brain with some regions of interest marked.

a. Strategic reasoning: The central feature of strategic thinking is the ability to forecast what other players will do purely by reasoning about their likely choices (and about the reasoning of others, and others’ reasoning about reasoning, etc.) An example which distinguishes pure strategic thinking from emotional forecasting and dynamic planning ahead (which are discussed separately below) is the “p-beauty contest game” (e.g., Ho et al, 1998, and named after a passage in John Maynard Keynes’s famous economics treatise about how the stock market is like a beauty contest). In this game each of the players chooses a number in the interval xi [0,100]. The player who is closest to p times the average (with p<1) wins a fixed payoff. The Nash equilibrium in this game is a number x which is close to the average of everyone else picking x, which is zero. Put differently, the only stopping point to the introspective iteration “If the average was X, I would pick (2/3)X; but if everyone else is as smart as me, where do we all stop?”…is zero.

In 24 different subject pools with p=2/3, the average number picked ranges from 20 to 35. These choices suggest that people are only doing 1 to 3 steps of strategic thinking on average (Camerer, Ho, and Chong, 2004).

The availability of a very large amount of data on these games enables us to construct an IQ item which gives a percentage chance that a person would win the game, if she played in a group sampled from previous data. The percentage chance of winning times the winning payoff gives a numerical score.[2]

Reasoning in this game requires people to use working memory to store iterations of reasoning (e.g. “If I think the average will be 50, I should choose 33; but if people think like I do they will pick 33 so I should choose 22…”). It also presumably requires “theory of mind” (ToM, e.g. Baron-Cohen 1995), the capacity to form beliefs about what other minds know, as well as the ability to iterate theory-of-mind beliefs.

Table 1: Strategic principles, exemplar games, cognitive processes, and candidate brain regions

Strategic principle / Exemplar game / Cognitive process / Brain regions to explore
Strategic reasoning / Beauty contest / Working memory, ToM / VM (pilot), DLPFC
Emotional anticipation / Trust / ToM (emotions), social emotion / VM, insula, cingulate (Sanfey et al 2003)
Strategic foresight / Shrinking-pie bargaining / Planning / BA 10, DLPFC
Coordination / Pure matching / ToM, social meta-knowledge / VM, BA8
Learning / Iterated beauty contest / Reinforcement, regret, forgetting, novelty-detection / VM (pilot), Hippocampus

b. Emotional anticipation:In the beauty contest game the payoff is fixed (in game theory jargon, the game is “constant-sum”) so there is little scope for emotional reaction to inequality in payoffs. In most games, however, the distribution of payoffs (and their total) depends on the choices peple make. A wide variety of data suggest people dislike unequal payoffs and will often sacrifice their own payoffs to reduce inequality (e.g., Fehr and Schmidt 1999), to harm a player who has treated them badly or help a player who has behaved nicely (e.g. Rabin, 1993). Therefore, a separate feature of strategic thinking is the ability to forecast how others will behave when emotions influence their reaction to unequal outcomes.

A well-studied exemplar[3] game is the “trust game” (Camerer and Weigelt, 1988). In the simplest version of this game (Berg et al, 1995) one player starts with $10 which she can partly invest, or keep. The amount she invests is tripled—representing a productive return on investment—and given to a second player, the “trustee”. The trustee can repay as much as she wants to the first player, or keep as much as she wants. Presumably trustees repay money because they feel a sense of altruism toward the first player, or a sense of reciprocal moral obligation since the first player took a risk to enlarge the available “pie” for both players. Therefore, the first player must anticipate the emotional reaction of the trustee—the trustee’s sense of altruism or reciprocity.

Many studies show that players invest about half of their $10 on average (although the initial investments are widely dispersed) and, on average, trustees repay about $5 so the first player just breaks even.

Investing wisely in trust games requires theory of mind as well as anticipation of social emotion. Studies of autistics (who are thought to have poor ToM) show that about a third do not anticipate emotional reactions of others (Hill and Sally, 2003). An fMRI study by Sanfey et al (2003) of the related “ultimatum” game shows that when the second player is deciding what to do, there is activity in prefrontal cortex, insula (a regionwhich is active in discomfort like disgusting odors and pain), and cingulate cortex (a “conflict resolution” region which weighs the desire to earn more money with emotional reactions to inequality). These studies provide candidate regions for emotional anticipation in strategic thinking we will explore in fMRI and with lesion patients.

c. Strategic foresight:The two games discussed so far are played simultaneously (the beauty contest game) or only require one step of planning (the trust game). Another component of strategic IQ is strategic foresight in games with many steps (in psychological terms, “planning”). Many studies suggest that players do not plan ahead more than a couple of steps.

An exemplar game is alternating-offer “shrinking pie bargaining”[4], a workhorse example widely used in economics and political science. In a three-stage example studied experimentally, one player (P1) makes an offer of a division of $5 between herself and a second player, P2. If P2 accepts the offer they earn the proposed amounts and the game ends. However, if P2 rejects the offer then the available money “shrinks”, say to $2.50, and P2 has a chance to make an offer of how to divide the $2.50. If P1 rejects P2’s offer the pie shrinks further, say to $1.25, and P1 makes a final offer. If P2 rejects that offer, the game ends and neither player earns anything.