Strategizing in the Brain

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Science  13 Jun 2003:
Vol. 300, Issue 5626, pp. 1673-1675
DOI: 10.1126/science.1086215

Most economic theories minimize the influence of human emotions and assume that what people believe and choose follows rationality principles. Important principles include knowing how much of one valuable good is worth one unit of another; following the rules of probability in processing information; planning ahead; resisting temptation; and guessing accurately what others will do. These principles have proved useful as mathematical building blocks for devising aggregate theories of corporate and market behavior. An emerging field of study called “behavioral economics” [HN1] takes advantage of dramatic advances in psychology and neuroscience. Behavioral economics replaces strong rationality assumptions with more realistic ones and explores their implications (1). A clear demonstration of how neural evidence contributes to behavioral economics is provided by Sanfey et al. [HN2] on page 1755 of this issue (2). These investigators analyzed subjects with functional magnetic resonance imaging [HN3] as they played the “ultimatum game,” [HN4] and correlated activity in certain brain areas with the cognitive and emotional processes involved in economic decision-making.

In their version of the ultimatum (or “take-it-or-leave-it”) game, a proposer offers a division of $10 to a responder, who accepts it (ending the game) or rejects it, leaving both players with nothing. The prediction is that responders who want to earn the most money will take any offer; a self-interested proposer who anticipates this will offer the smallest amount. However, this prediction turns out to be wrong (offers are typically around 50% of the total amount, and 50% of low offers are rejected). Functional magnetic resonance imaging shows why. Subjects whose brains were imaged while they were presented with an unfair offer ($1 to $2 out of the $10 available) showed greater activity in the bilateral anterior insula [HN5] of the brain, revealing that such an offer created negative emotions. Those subjects with the strongest activation of the anterior insula rejected a higher proportion of unfair offers. The anterior cingulate (ACC) [HN6], a brain region that detects cognitive conflict, also showed greater activity during presentation of an unfair offer, suggesting that this area mediates the conflict between earning money and feeling bad. These findings emphasize the importance of emotional influences in human decision-making.

In games like ultimatum bargaining, “players” with information choose “strategies” that, collectively, create outcomes that players like or dislike and to which they attach numerical valuations (“utilities” [HN7]). Game theory [HN8] can link economics to other sciences because it uses the same tools to model interactions at many different scientific levels (genes, firms, nation-states). But doing so requires extending the central assumptions of rational game theory, namely, that players are (i) self-interested and (ii) reach an “equilibrium” in which everyone is choosing (or planning) strategies that yield the best outcome, anticipating that others are doing the same. An emerging approach called “behavioral game theory” [HN9] replaces these assumptions with precise alternatives that are more cognitively plausible (3).

One ingredient of behavioral game theory is a model of “social utility,” showing how players' utilities for payoff allocations depend on how much others get, as well as on their own payoffs. This old idea is illustrated by many experiments showing that people routinely cooperate in the “prisoner's dilemma” game [HN10], in which “defection” is always better for one player but mutual “cooperation” makes everyone in a group better off. Prisoner's dilemma cooperation is well established, but evidence from newer games (like ultimatum bargaining) help to calibrate precise social utility functions that make fresh predictions (4).

One new game is “trust.” [HN11] In a trust game, one player can invest money that is multiplied (say, by 3) to reflect the investment's productivity. A second trustee player can repay or keep as much of the tripled investment as he or she likes. The baseline game is played with anonymous strangers, as a model of investment in economies with “country risk” and poor legal protection for investors, or firms paying wages and trusting employees to work hard (4). When the trust game is played once, the first player usually invests about half and is repaid roughly what he or she invested (3). Trustworthiness correlates with the trustee's level of oxytocin [HN12] after being trusted, a hormone important in social bonding (5), and also correlates with economic growth across economies. Mutual cooperation in the prisoner's dilemma also leads to increased cortical activation, suggesting a neural location for the “warm glow” of receiving reciprocation (6). When the trust game is played a fixed number of times, players invest and repay in early periods, but trust breaks down when the repeated game's end grows near (3).

Theories of social utilities that include guilt from getting more than others, and envy from getting less, predict rejections of low ultimatum offers to reduce envy, and repayment of trust to reduce guilt (3, 4). The Sanfey et al. results provide a neural foundation for these models, by locating distaste for envy in the insula, and the trade-off between envy and money in the ACC. Competing theories focus on the human instinct to reciprocate, and the idea that one-shot games are an “unnatural habitat” for humans who evolved playing repeated games in close-knit groups (3).

The rejections Sanfey et al. report in their ultimatum game are typical. But results from special populations illuminate the boundary of this regularity and its causes. Autistic adults (7) and players in some small-scale societies (8) offer less and accept very little, which suggests, ironically, that rational game theory only works in ultimatum games when deficits in “mind reading” or cultural adaptation lead to extremely uneven offers. Cooperativeness in normal subjects is also correlated with heightened activity in the prefrontal cortex (Brodmann area 10), implicated in mind reading, and with limbic activity (9) [HN13].

A second ingredient of behavioral game theory is the idea that players use only one or two steps of iterated strategic reasoning (3, 10). Limited strategizing is illustrated by the “beauty contest” game [HN14], in which players choose numbers from 0 to 100, and the player whose number is closest to two-thirds of the average wins a fixed prize. Rational game theory predicts an equilibrium in which choices are mutually consistent (leading to 0), but in experiments many players assume that others are making random choices, and choose 33, or believe that others are responding to random choices, and choose 22. Models of this cognitive hierarchy organize regularity from many games and show that one or two steps of thinking are typical, although three or four steps are used by analytically skilled undergraduates and game theorists (10, 11).

A third ingredient of behavioral game theory is learning: Simple parametric models of generalized reinforcement explain learning paths in dozens of games (12). These models are supported by studies showing that accumulated reinforcement correlates with single-neuron parietal activity in monkeys making rewarding eye saccades (13). But some human players are “sophisticated”; they realize that others are learning and choose strategies that build beneficial reputations, like repaying early in trust games that are repeated (3, 11).

Studies of alternating-offer bargaining illustrate all three ingredients. Consider a three-stage game in which the players first bargain over a $5 “pie.” If the first player's offer is rejected, the second player gets to make a counteroffer, dividing $2.50; if that offer is rejected player 1 makes a final (ultimatum) counteroffer, dividing $1.25 (see the figure) (14). Game theory predicts that the self-interested first player who plans ahead will offer $1.25. In experiments, opening offers are more generous, $2 to $2.50, and lower offers are rejected half the time. Measuring attention in computer displays shows that most players barely look ahead, or look only one stage ahead. Players who spontaneously look further ahead or are trained to do so make offers closer to the rational game theory prediction.

Planning ahead when bargaining.

The diagram explains the workings of a “bargaining game” equivalent to a stretched-out version of the ultimatum game described by Sanfey et al. (2). The four columns of vertically arrayed boxes (white) each represent the payoff in one stage of a three-stage bargaining game with alternating offers (top box is round 1, bottom box is round 3). In stage 1 (top box) players divide $5; in stage 2 they divide $2.50; in stage 3 they divide $1.25 (if the third-stage offer is rejected they earn nothing). The shaded regions of boxes show the relative time in which each box is clicked open to reveal the payoff in that stage, the relative number of times each box is opened (box width), and the relative number of forward (down arrow) and backward (up arrow) transitions between stages (arrow thickness; average transitions of less than one per trial omitted). Columns (from left) show what happens when players look most often at the first box (level 0 thinking), look more often at the second box than the first (level 1 thinking), look more often at the third and second than the first (equilibrium), and when subjects are trained in backward induction (trained). Bottom histograms show frequency distributions of offers from players whose looking times correspond to each of the four patterns. Dotted vertical lines show an even $2.50 offer (right vertical line) and the game-theoretic (“perfect”) equilibrium $1.25 offer (left vertical line). Looking more often at later-stage boxes (in columns 2 and 3) shifts offer distributions to the left, toward the rational game theory prediction of $1.25.

Constrained by these facts, game theory is trifurcating into three approaches: rational game theory, useful for modeling firms and countries that pool cognitive resources and hire consultants to analyze games carefully (for example, bidding for telecommunications spectrum in auctions); behavioral game theory, useful for explaining what normal people do and how they learn, which is important for explaining strikes, divorces, incentive contracts, and litigation; and evolutionary game theory [HN15], which explains equilibration in animal populations by natural selection, and imitation among humans (social selection).

Informing game theory is only one way in which neuroscience will reshape economics. Other puzzles that neuroeconomics can help to solve include the fact that people find some trade-offs between health, time, statistical lives, clear air, and money difficult or offensive; how advertising works; the fact that many people do not plan lifetime savings optimally, or succumb to ruinous temptation and addiction; and the fact that financial markets and macroeconomies fluctuate so dramatically (15).

HyperNotes Related Resources on the World Wide Web

General Hypernotes

Dictionaries and Glossaries

The xrefer Web site provides scientific dictionaries and other reference works.

A neuroscience glossary is provided by the Neuroscience at a Glance Companion Web site.

A glossary of terms is provided by the University of Utah's HyperBrain Web site.

Definitions of economic and game theory terminology are provided by

Web Collections, References, and Resource Lists

The Google Web Directory provides a collection of links to Internet neurobiology, economics, and game theory resources.

Neurosciences on the Internet ( is a searchable and browsable index of Internet neuroscience resources maintained by N. Busis, Division of Neurology, UMPC Shadyside Hospital, Pittsburgh.

Neuroanatomy & Neuropathology on the Internet is an extensive collection of resources and Internet links maintained by K. Hegedüs, Department of Neurology, University of Debrecen, Hungary.

NeuralLinksPlus is collection of Internet links provided by M. Dubin, Department of Molecular, Cellular, and Developmental Biology, University of Colorado.

The Social Science Information Gateway provides links to Internet resources on game theory. provides links to Internet resources related to functional magnetic resonance imaging.

Online Texts and Lecture Notes

Kimball's Biology Pages, an online biology textbook and glossary, includes an introduction to the human brain and nervous system.

S. Kornguth, Department of Neurobiology and Institute for Advanced Technology, University of Texas, provides lecture notes for a neuroscience course on the brain.

The Centre for Psychology, Athabasca University, Canada, provides biological psychology tutorials.

ELSE (ESRC Centre for Economic Learning and Social Evolution) at University College London provides a working paper series that brings together theoretical, experimental, and empirical research in anthropology, biology, economics, and psychology.

CyberEconomics is an introductory online economics textbook by R. Schenck, Saint Joseph's College, Rensselaer, IN.

The Economic and Game Theory Web page by D. Levine, Department of Economics, University of California, Los Angeles, provides general interest materials on game theory, as well as research papers on economic theory, mathematical economics, and game theory.

R. A. McCain, Department of Economics and International Business, Drexel University, makes available a hypermedia economics textbook. A chapter on imperfect competition and game theory is included.

S. Quartz, Division of Humanities and Social Sciences, California Institute of Technology, makes available readings for a course (taught with C. Camerer) on the neural foundations of social science.

The UCLA Brain Mapping Center makes available readings and other resources for a course on functional neuroimaging.

P. Zak, Center for Neuroeconomics Studies, Claremont Graduate University, provides a neuroeconomics reading list.

General Reports and Articles

The 29 January 2003 issue of the Princeton Alumni Weekly had an article by Billy Goodman titled “New brain research helps explain how we do-and don't-reason.”

P. Glimcher, Center for Neural Science, New York University, makes available (in PDF format) his 10 October 2002 Neuronarticle titled “Decisions, decisions, decisions: Choosing a neurobiological theory of choice.”

The Interdisciplinary Center for Economic Science, George Mason University, provides in PDF format an encyclopedia article by V. Smith titled “Experimental methods in (neuro)economics.”

C. Camerer makes available (in PDF format) a research paper by C. Camerer, G. Loewenstein, and D. Prelec titled “Neuroeconomics: How neuroscience can inform economics” and a May 2003 article titled “Behavioural studies of strategic thinking in games.”

M. Rabin, Department of Economics, University of California, Berkeley, makes available in PDF format a 1997 working paper titled “Psychology and economics.”

Numbered Hypernotes

1. Behavioral economics. Behavioral economics is defined in the glossary provided by the Sonderforschungsbereich (SBF) 504, University of Mannheim, Germany. The 14 September 1999 issue of the Proceedings of the National Academy of Sciences had an article by C. Camerer titled “Behavioral economics: Reunifying psychology and economics.” C. Camerer makes available in PDF format the draft chapter by C. Camerer and G. Loewenstein titled “Behavioral economics: Past, present, future” that introduces the forthcoming book Advances in Behavioral Economics.

2. A. G. Sanfey, J. K. Rilling, L. E. Nystrom, and J. D. Cohen are at the Center for the Study of Brain, Mind, and Behavior, Princeton University. J. A. Aronson is at the Department of Psychology, Princeton University. Cohen and Nystrom's Neuroscience of Cognitive Control Laboratory at Princeton has a home page with publications available in PDF format.

3. Functional magnetic resonance imaging (fMRI). The Society for Neuroscience offers an article on brain imaging. The PBS Secret Life of the Brain Web site includes a presentation on scanning the brain with MRI. A student project on MRI was prepared for a course on brain, thought, and action taught by M. Dubin. The Functional MRI Research Center, Columbia University, offers a presentation on fMRI; a collection of readings (in PDF format) is provided for an fMRI course. Princeton University's Center for the Study of Brain, Mind, and Behavior offers a presentation on its neuroimaging facility. J. Hornak, Magnetic Resonance Laboratory, Rochester Institute of Technology, provides an MRI tutorial with a section on fMRI. offers an article by T. Gregg titled “Use of functional magnetic resonance imaging to investigate brain function.” The 14 September 2001 issue of Science had a report by J. Greene et al. titled “An fMRI investigation of emotional engagement in moral judgment.”

4. The ultimatum game. The Evolving Artificial Moral Ecologies Project at the Centre for Applied Ethics, University of British Columbia, offers a presentation on the ultimatum game. The Interactive Decision Laboratory, Center for Rationality and Interactive Decision Theory, Hebrew University, offers a presentation on the ultimatum bargaining game. J. Duffy, Department of Economics, University of Pittsburgh, offers slide lecture notes on “take it or leave it” bargaining games for a course on game theory. M. Rabin discusses the ultimatum game in a 1997 working paper (available in PDF format) titled “Bargaining structure, fairness, and efficiency.” The 8 September 2000 issue of Science had a report by M. Nowak, K. Page, and K. Sigmund titled “Fairness versus reason in the ultimatum game.”

5. Insula. Insula is defined (and Internet links provided) in the Anatomy of the Brain presentation from About Biology. The Medcyclopaedia defines insula. BrainInfo provides information on the insula. The location of the insula is indicated in the atlas of neuroanatomy structures provided by Neuroanatomy & Neuropathology on the Internet. The University of Iowa's Virtual Hospital provides annotated images (one and two) of the insula. An image of the insula is provided by the Department of Anatomy and Neurobiology, University of Arkansas for Medical Sciences. BBC News offers a 1 June 1998 article titled “Brain links taste and disgust.”

6. Anterior cingulate cortex (ACC). The Department of Physiology, University of Oklahoma Health Sciences Center, provides a study aid diagram of the location of the cingulate cortex. The Centre for Psychology, Athabasca University, provides an introduction to the cingulate gyrus in a tutorial on the limbic system. offers a presentation on the cingulate gyrus. provides illustrations of the activation of the ACC and other areas of the brain in a feature on the science of love. The Cohen Lab makes available in PDF format a 2001 NeuroImage article by V. van Veen et al. titled “Anterior cingulate cortex, conflict monitoring, and levels of processing.” The 15 February 2002 issue of the Proceedings of the National Academy of Sciences had an article by C. Carter et al. titled “Parsing executive processes: Strategic versus evaluative functions of the anterior cingulate cortex.” G. Bush, Cingulate Cortex Research Laboratory, Massachusetts General Hospital, makes available (in PDF format) a 2000 Trends in Cognitive Sciences review article by G. Bush, P. Luu, and M. Posner titled “Cognitive and emotional influences in anterior cingulate cortex.” The 22 March 2002 issue of Science had a report by W. Gehring and A. Willoughby titled “The medial frontal cortex and the rapid processing of monetary gains and losses” and a News of the Week article by G. Miller titled “The good, the bad, and the anterior cingulate.”

7. Utility is defined in xrefer's Penguin Dictionary of Economics. Utility theory is defined by the University of Michigan's Decision Consortium.

8. Game theory. The SBF 504 glossary includes an introduction to game theory. The online Stanford Encyclopedia of Philosophy has an article on game theory. D. Levine's Economic and Game Theory Web site offers an introduction to game theory and an encyclopedia article on game theory. The History of Economic Thought Website, provided by the Department of Economics, New School University, New York, offers an essay on game theory. R. A. McCain provides a tutorial on game theory. A. Roth, Department of Economics, Harvard University, provides a game theory and experimental economics Web page. provides resources and Internet links related to game theory.

9. Behavioral game theory. Princeton University Press makes available the introductory chapter of C. Camerer's 2003 book Behavioral Game Theory: Experiments in Strategic Interaction. C. Camerer makes available in PDF format a paper by C. F. Camerer, T.-H. Ho, and J. K. Chong titled “Behavioral game theory: Thinking, learning, and teaching.”

10. Prisoner's dilemma game. has an introduction to the prisoner's dilemma and provides applets to play it. The online Stanford Encyclopedia of Philosophy has an article on the prisoner's dilemma. Principia Cybernetica Web offers a presentation on the prisoners' dilemma game. R. Schenck's CyberEconomics includes a discussion of the prisoner's dilemma. R. A. McCain's tutorial on game theory includes a presentation on the prisoner's dilemma. S. Helfrich offers a prisoner's dilemma applet.

11. The trust game is discussed in an article in the 10 May 2003 New Scientist by K. Grimes titled “To trust is human,” which P. Zak makes available in PDF format.

12. Oxytocin. Oxytocin is defined in xrefer's Dictionary of Biology. Online Mendelian Inheritance in Man has an entry for oxytocin. A presentation on oxytocin is included in a student project prepared for a course on neural systems and animal behavior taught by C. Hopkins, Department of Neurobiology and Behavior, Cornell University. S. Carter, Department of Psychiatry, University of Illinois, Chicago, discusses oxytocin in a lecture slide presentation on the neurobiology of social behavior for a course on brain and behavior. The Biology of the Mammary Gland Web site makes available a review by W. S. Young titled “Oxytocin and its role in reproduction and behavior.”

13. Brodmann areas. M. Dubin provides a presentation on Brodmann areas. The UCLA Brain Mapping Center offers illustrations of the location of Brodmann areas of the brain for a functional neuroanatomy course. P. McCaffrey, Speech Pathology Graduate Program, California State University, Chico, offers lecture notes on cerebral lobes, cerebral cortex, and Brodmann areas for a neuroanatomy course. The 25 September 2001 issue of the Proceedings of the National Academy of Sciences had an article by K. McCabe et al. titled “A functional imaging study of cooperation in two-person reciprocal exchange” that discusses the link between cooperation and activation of Brodmann area 10.

14. The beauty contest game. M. Shor, Owen Graduate School of Management, Vanderbilt University, offers a presentation on the beauty contest game for a game theory course. The Royal Economic Society provides a media briefing titled “Mr Keynes' ‘beauty contests’: How bad we are at guessing games.” The Fall 1999 issue of the newsletter Classroom Expernomics had an article by R. Nagel titled “A Keynesian beauty contest in the classroom.” D. Laibson, Department of Economics, Harvard University, discusses the beauty contest game (PDF-format lectures one and two) in lecture notes for a course on psychology and economics.

15. An article about evolutionary game theory is included in the Stanford Encyclopedia of Philosophy. A tutorial on evolutionary game theory is provided by K. Prestwich, Department of Biology, College of the Holy Cross. C. Hauert, Institute for Mathematics, University of Vienna, offers virtual labs in evolutionary game theory.

16. C. F. Camerer is in the Division of Humanities and Social Sciences, California Institute of Technology.


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