Neuroeconomics Decision Making And The Brain

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NeuroeconomicsDecision Making and the BrainEdited byPaul W. Glimcher, PhDCenter for NeuroeconomicsNew York UniversityNew York, NY, USAColin F. Camerer, PhDDivision of Humanities and Social SciencesCalifornia Institute of TechnologyPasadena, CA, USAErnst Fehr, PhDInstitute for Empirical Research in EconomicsUniversity of ZürichZürich, SwitzerlandRussell A. Poldrack, PhDDepartment of PsychologyUniversity of California Los AngelesLos Angeles, CA, USAAMSTERDAM BOSTON HEIDELBERG LONDONNEW YORK OXFORD PARIS SAN DIEGOSAN FRANCISCO SINGAPORE SYDNEY TOKYOAcademic Press is an imprint of Elsevier

C H A P T E R31Mechanisms for Stochastic Decision Makingin the Primate Frontal Cortex: Single-neuronRecording and Circuit ModelingDaeyeol Lee and Xiao-Jing WangO U T L I N EIntroduction481Game-theoretic Studies of Decision Making inNon-human PrimatesGame Theory and Learning in SocialDecision MakingChoice Behavior During a Matching Pennies GameChoice Behavior During a Rock–Paper–ScissorsGameNeurophysiological Studies of Decision Makingin Competitive GamesRole of the Dorsolateral Prefrontal Cortex inDecision MakingRole of the Anterior Cingulate Cortex inDecision MakingModels of Decision MakingDrift-diffusion, Leaky Competing Accumulator,and Attractor Network ModelsWhat is Spiking Network Modeling?A Recurrent Circuit Mechanism ofDecision MakingNeural substrate of a Decision Threshold483483484492494Reward-dependent Plasticity and AdaptiveChoice BehaviorComputation of Returns by SynapsesMatching Law: Melioration Versus OptimizationRandom Choice Behavior in MatchingPennies gments500References500490490INTRODUCTIONanimals seldom behave solely based on their intrinsic metabolic needs, as sensory information about theenvironment must be taken into account in determining which action the animal should produce to obtainthe most desirable outcomes. Sensory inputs arealways noisy, and perceptual analysis of these inputsDecision Making refers to the process of evaluating the desirabilities of alternative choices and selecting a particular option. Thus, many brain functionscan be characterized as decision making. For instance,Neuroeconomics: Decision Making and the Brain491481 2009, Elsevier Inc.

48231. MECHANISMS FOR STOCHASTIC DECISION MAKING IN THE PRIMATE FRONTAL CORTEXreduces the uncertainty about the nature of sensorystimuli encountered in the animal’s environment inorder to categorize stimuli and select the most likelyinterpretation of the world. Once the relevant stimuliin the animal’s environment are properly interpreted, itis then necessary to evaluate the desirability of the outcome expected from each of the alternative behavioralplans. Finally, even when the behavioral goal is set, aparticular spatio-temporal sequence of muscle activation must be chosen to carry out the desired action.Theoretical analyses of steady-state choice behavior are often formulated based on the principles ofoptimality and equilibrium. For example, game theoryseeks to describe optimal decision-making strategies formultiple decision makers trying to maximize their ownself-interests through a variety of complex social interactions (von Neumann and Morgenstern, 1944; Nash,1950; see also Chapter 5 for an introduction to gametheory). However, such approaches are limited whenthe decision makers do not possess all the information about the environment, or when the environmentchanges frequently. In such cases, the decision makersmay need to improve their decision-making strategiesincrementally by trial and error. This is often referredto as melioration (Herrnstein et al., 1997). Similarly, models based on reinforcement learning (Sutton and Barto,1998) have been developed to account for how variouschoice behaviors change dynamically.Neuroeconomics applies a variety of techniquesto investigate the biological processes responsible fordecision making. Among them, physiological techniques that probe the activity of individual neurons atmillisecond temporal resolution are generally applicable only to animals, due to their invasive nature.Fore-periodDelayIn particular, non-human primates can be trained toperform relatively complex decision-making tasks, andtheir choice behaviors display many features similar tohuman choice behaviors. Since the brains of these twospecies display many structural and functional similarities, the results of single-neuron recording experiments conducted in non-human primates can providevaluable insights into the basic neural circuit mechanisms of decision making in humans. In recent years,electrophysiological studies in behaving monkeyshave begun to uncover single-neuron activity that iscorrelated with specific aspects of perceptual decisionmaking and reward-dependent choice behavior. Forinstance, Shadlen and his colleagues used a perceptualdecision-making task based on random dot motiondirection discrimination (Figure 31.1a), and found thatactivity of individual neurons in the primate posteriorparietal cortex reflects the process of accumulatingevidence (Roitman and Shadlen, 2002). Others (Surgueet al., 2004; Lau and Glimcher, 2005) examined thechoice behavior of monkeys during a decision-makingtask based on concurrent schedules of reinforcement(Figure 31.1b), and found that their choice behaviorlargely conformed to the predictions of the matchinglaw (Herrnstein et al., 1997). Furthermore, the activityof neurons in the posterior parietal cortex encodedthe rate of reward or utility expected from a particularchoice (Dorris and Glimcher, 2004; Sugrue et al., 2004).In contrast to perceptual discrimination tasks and concurrent schedules of reinforcement, competitive gamesinvolve interactions among multiple decision agents.It has been shown that monkeys are capable of producing stochastic choice behaviors that are nearly optimal for such competitive games (Dorris and Glimcher,MotionChoice(a) Random-dot motion direction discrimination oiceReward(b) Concurrent schedules of reinforcementFIGURE 31.1Decision-Making tasks used in monkeys. (a) A random-dot motion discrimination task. When the animal fixates a centraltarget, two peripheral choice targets are presented. Then, random-dot motion stimuli are presented, and the animal is required to shift its gazetowards one of the choice targets according to the direction of random-dot stimuli. (b) During a decision-making task based on concurrentreinforcement schedules, each target is baited with a particular probability (variable rate) or after a time interval sampled from a particulardistribution (variable interval).V. THE NEURAL MECHANISMS FOR CHOICE

GAME-THEORETIC STUDIES OF DECISION MAKING IN NON-HUMAN PRIMATES2004; Lee et al., 2004, 2005). During such tasks, neuronsin the dorsolateral prefrontal cortex and the anteriorcingulate cortex exhibited firing activity that reflectedhistory of past choice and rewards (Barraclough et al.,2004; Seo and Lee, 2007; Seo et al., 2007).These experiments have spurred theoretical workthat uses mathematical approaches to illuminateexperimental observations. For instance, accumulator models have been widely applied to perceptualdecision making (Smith and Ratcliff, 2004; Gold andShadlen, 2007; see also Chapter 4). Reward-basedchoice behavior has been described by reinforcementlearning models (Sutton and Barto, 1998; see alsoChapter 22). We will briefly summarize these modelsin relationship to our neurophysiological recordingexperiments in non-human primates. Our focus,however, will be neural circuit modeling, whichattempts to go one step further and explore how decision behavior and correlated neural activity can beexplained by the underlying circuit mechanisms. Forexample, what are the neural circuit substrates fortime integration of sensory evidence about alternative choices and for action selection? Is valuation ofactions instantiated by neurons or synapses, and howdoes a neural circuit make dynamic decisions adaptively over time? What are the sources of stochasticity in the brain that underlie random choice behavior?We will introduce neural circuit models and illustratetheir applications to a perceptual discrimination task(Wang, 2002; Machens et al., 2005; Lo and Wang, 2006;Wong and Wang, 2006; Miller and Wang, 2006), aforaging task based on concurrent schedules of reinforcement (Soltani and Wang, 2006), and a matchingpennies game task (Soltani et al., 2006). These computational studies showed that a general neural circuitmodel can reasonably account for salient behavioraland electrophysiological data from diverse decisiontasks, suggesting common building blocks of decisionmaking circuitry that may be duplicated throughoutdifferent stages of sensori-motor transformation in theprimate brain.GAME-THEORETIC STUDIES OFDECISION MAKING IN NON-HUMANPRIMATESGame Theory and Learning in SocialDecision MakingWhen each of the alternative actions produces aparticular outcome without any uncertainty, optimaldecision making consists simply of choosing the action483that produces the most desirable outcome. When thereis uncertainty about the outcomes expected from various actions, the animal’s choice should be influencedby the likelihood of desirable outcomes expected fromeach action. A large number of economic theories,such as the expected utility theory (von Neumann andMorgenstern, 1944) and prospect theory (Kahnemanand Tversky, 1979), have been proposed to accountfor such decision making under uncertainty or risk. Inreality, however, the environment changes constantly,and this frequently alters the likelihood of various outcomes resulting from different actions. Consequently,optimality is rarely achieved, and typically subjectscan only approximate optimal decision strategies bylearning through experience (Sutton and Barto, 1998).The complexity and hence difficulty of such learning would depend on the nature of dynamic changesin the animal’s environment, which can occur fora number of reasons. Some are cyclical, such as seasonal changes, and others are predictable changesresulting from the animal’s own actions, such as thedepletion of food and other resources. Animals livingin social groups face even more difficult challenges,because competitive interactions with other animalstend to make it quite difficult to predict the outcomesresulting from their own actions. Nevertheless, decision making in such social settings provides a uniqueopportunity to test various theories about the behavioral dynamics and underlying mechanisms of decision making.One way to tackle mathematically the problems ofdecision making in a social context is formulated bygame theory (von Neumann and Morgenstern, 1944;see also Chapter 5 of this volume). In game theory, agame is specified by a particular number of decisionmakers or players, a list of alternative choices available to each player, and the payoff matrix that assigns aparticular outcome or payoff to each player accordingto the combination of actions chosen by all players.In other words, the payoff given to a player does notdepend simply on that player’s own action, but onthe actions of all players in the game. In addition,a strategy for a given player is defined as a probability distribution over a set of available choices.A pure strategy refers to choosing a particular actionexclusively, whereas a mixed strategy refers to acase in which multiple actions are chosen with positive probabilities. One of the predictions from gametheory is that a set of players trying to maximize theirself-interests would converge onto a set of strategiesknown as Nash Equilibrium, which is defined as a setof strategies for all players that cannot be changed byany individual player to increase his payoff. A gameis called a mixed-strategy game when its equilibriumV. THE NEURAL MECHANISMS FOR CHOICE

48431. MECHANISMS FOR STOCHASTIC DECISION MAKING IN THE PRIMATE FRONTAL CORTEXstrategy is mixed. In addition, a game is referred to aszero-sum when the sum of the payoffs for all playersis always zero, so that someone’s gain necessarilymeans someone else’s loss. In the following sections,we describe the results from behavioral experimentsto illustrate that non-human primates can approximate the mixed equilibrium strategies through iterative learning algorithms in competitive zero-sumgames with two and three alternative actions. Thesecorrespond to the familiar games of matching penniesand Rock–Paper–Scissors, respectively.When two rational players participate in the matching pennies game, the Nash Equilibrium is for eachplayer to choose the two targets with equal probabilities and independently across successive trials. Anyother strategy could be exploited by the opponent.In the monkey experiment, the strategy of the computer opponent was systematically manipulated todetermine how the animal’s choice behavior wouldbe affected by the strategy of its opponent. Initially,the computer opponent chose the two targets with thesame probabilities, regardless of the animal’s choices.This was referred to as algorithm 0, and correspondedto the Nash Equilibrium strategy pursued unilaterally without regard to the opponent’s behavior. Inthis case, the animal’s expected payoff would be fixedregardless of how it chose its target. Therefore, it wasnot surprising that all three monkeys tested with algorithm 0 displayed a strong bias to choose one of thetwo targets more frequently. Overall, the monkeys C,E, and F chose the right-hand target in 70.0%, 90.2%,and 33.2% of the trials, respectively. In the next stageof the experiment, the computer opponent applied aset of statistical tests to determine whether the animal’s choice was randomly divided between the twotargets. If not, the computer decreased its probabilityof choosing a particular target as the animal chose thesame target more frequently. This was referred to asalgorithm 1. Importantly, this algorithm did not examine the animal’s reward history, and therefore was notsensitive to any bias that the animal might show inusing the information about its previous rewards todetermine its future choices. When tested with algorithm 1, the animals chose the two targets more orless equally frequently. Overall, during algorithm 1,the monkeys C, E, and F chose the right-hand targetChoice Behavior During a MatchingPennies GameTo test whether and how monkeys approximatedoptimal decision-making strategies in simple competitive games through experience, previous studies haveexamined the choice behavior of monkeys in a computer-simulated binary zero-sum game, commonlyreferred to as matching pennies (Lee et al., 2004; Figure31.2a). In this game, each of two players chooses fromtwo alternative options, and one of the players winsif his choices match and loses otherwise. During theexperiment, a monkey was required to begin eachtrial by fixating a small yellow square presented in thecenter of a computer screen. Shortly thereafter, twoidentical green disks were presented along the horizontal meridian, and the animal was required to shiftits gaze towards one of the targets when the central fixation target was extinguished. The computer opponentalso chose its target according to a pre-specified algorithm described below, and the animal was rewardedonly when it chose the same target as the computer(Figure 31.2b).Monkey CMonkey EComputerLeftRightRightLeft01LeftComputer selects: 0.7Monkey F0.60.50.421(a)(b)FIGURE 31.2(c)AlgorithmMonkey’s choice behavior during the matching pennies game.(a) During this task, the animal made a saccadic eye movement towards one of the two peripheral targets to indicate its choice and was rewarded only when it chose the same target as the computeropponent. (b) The payoff matrix for the matching pennies game. (c) The probability that the animal would choose its target according to theso-called win–stay–lose–switch strategy during the matching pennies game against the computer opponent programmed with two differentalgorithms (1 and 2).V. THE NEURAL MECHANISMS FOR CHOICE

GAME-THEORETIC STUDIES OF DECISION MAKING IN NON-HUMAN PRIMATESin 48.9%, 51.1%, and 49.0% of the trials, respectively.In addition, the animal’s successive choices were relatively independent, and as a result, the animal’s overall reward rate was close to the optimal value of 0.5(Lee et al., 2004). Interestingly, the animals were morelikely to choose the same target in the next trial if itwas rewarded in a given trial (win–stay) and switchto the other target otherwise (lose–switch). Such strategies were not penalized during the period of algorithm 1, since the information about the animal’sreward history was not utilized by the computeropponent. All three animals chose their targets according to this so-called win–stay–lose–switch (WSLS)strategy substantially more than in 50% of the trials(Figure 31.2c).In reinforcement learning models (Sutton andBarto, 1998; Camerer, 2003), the animal’s choice ismodeled by a set of value functions that are adjustedaccording to the outcome of the animal’s choice. Totest whether the animal’s choice during the matchingpennies game was accounted for by a reinforcementlearning model, the value function at trial t for a giventarget x, Vt(x), was updated after each trial accordingto the following (Lee et al., 2004):Vt 1 (x ) α Vt (x ) Δt (x )(31.1)where x L and R for the right-hand and left-handtargets, respectively, α is a decay factor, and Δt(x)reflects a change in the value function that dependson the outcome of a choice. It was assumed that ifthe animal chose the target x, the value function forx was adjusted according to whether the animal wasrewarded or not. Namely, when the animal selectedthe target x in trial t, Δt(x) Δrew if the animal wasrewarded, and Δt(x) Δunrew otherwise. For the target not chosen by the animal, Δt(x) 0. The probability that the animal would select the right-hand targetwas then determined by the following softmax rule:pt (R) exp Vt (R)/{exp Vt (R) exp Vt (L)}(31.2)The model parameters, α, Δrew, and Δunrew wereestimated using a maximum likelihood procedure(Pawitan, 2001). This reinforcement learning modelwas compared with an alternative model based onthe WSLS strategy. This WSLS model assumed thatthe animal chooses its target in each trial accordingto the WSLS strategy with some probability, pWSLS.For example, if the animal was rewarded for choosing a particular target in the previous trial, this modelassumes that the animal would choose the sametarget in the current trial with the probability of pWSLS.If the animal was not rewarded in the previous trial, it485would switch to the other target with the same probability. Whether the animal’s choice behavior wasbetter accounted for by the reinforcement learningmodel or the WSLS model was determined by theBayesian Information Criterion (BIC), defined asBIC log 2 log L k log N(31.3)where L denotes the likelihood of the model, k thenumber of model parameters (k 1 and 3 for theWSLS model and reinforcement learning model,respectively), and N the number of trials (Hastie et al.,2001). For each session, the model that minimizedthe BIC was chosen as the best model. The results ofmodel-fitting showed that for the reinforcement learning model applied to the choice data obtained withalgorithm 1, the value functions for a given targettended to increase (decrease) when the animal was(not) rewarded for choosing the same target (Figure31.3). In addition, the reinforcement learning modelperformed better than the WSLS model in 56.0% of thesessions (70/125 sessions). Therefore, for algorithm 1,the performance of these two models was comparable,suggesting that the animal’s choice was largely determined by the WSLS strategy.The same animals were then further tested againsta third computer opponent which tested not onlywhether the animal’s choice sequences were random,but also whether the a

Game-theoretic Studies of Decision Making in Non-human Primates 483 Game Theory and Learning in Social Decision Making 483 Choice Behavior During a Matching Pennies Game 484 Choice Behavior During a Rock–Paper–Scissors Game 485 Neurophysiological Studies of Decision Making in Competitive Games

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