1Section of Comparative Medicine, Yale School of Medicine, 2Department of Neurobiology, Yale School of Medicine, 3Center for Neural Science, New York University, 4Department of Psychology, New York University, 5Department of Economics, New York University
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Levy, I., Rosenberg Belmaker, L., Manson, K., Tymula, A., Glimcher, P. W. Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods. J. Vis. Exp. (67), e3724, doi:10.3791/3724 (2012).
Most of the choices we make have uncertain consequences. In some cases the probabilities for different possible outcomes are precisely known, a condition termed "risky". In other cases when probabilities cannot be estimated, this is a condition described as "ambiguous". While most people are averse to both risk and ambiguity1,2, the degree of those aversions vary substantially across individuals, such that the subjective value of the same risky or ambiguous option can be very different for different individuals. We combine functional MRI (fMRI) with an experimental economics-based method3 to assess the neural representation of the subjective values of risky and ambiguous options4. This technique can be now used to study these neural representations in different populations, such as different age groups and different patient populations.
In our experiment, subjects make consequential choices between two alternatives while their neural activation is tracked using fMRI. On each trial subjects choose between lotteries that vary in their monetary amount and in either the probability of winning that amount or the ambiguity level associated with winning. Our parametric design allows us to use each individual's choice behavior to estimate their attitudes towards risk and ambiguity, and thus to estimate the subjective values that each option held for them. Another important feature of the design is that the outcome of the chosen lottery is not revealed during the experiment, so that no learning can take place, and thus the ambiguous options remain ambiguous and risk attitudes are stable. Instead, at the end of the scanning session one or few trials are randomly selected and played for real money. Since subjects do not know beforehand which trials will be selected, they must treat each and every trial as if it and it alone was the one trial on which they will be paid. This design ensures that we can estimate the true subjective value of each option to each subject. We then look for areas in the brain whose activation is correlated with the subjective value of risky options and for areas whose activation is correlated with the subjective value of ambiguous options.
1. Preparing the Experiment
2. Preparing the Subject
4. Payment Procedure
For example, if the selected trial presented the lottery depicted in Figure 2 (an ambiguous lottery, offering $18 if a red chip is drawn) and the subject chose this lottery (rather than the reference lottery), then the subject should draw a chip out of the physical bag corresponding to the lottery image. If a red chip is drawn the subject will receive $18, if a blue chip is drawn they will receive nothing.
5. Analyzing the Behavioral Data
Where Pv is the probability that the subject chose the variable lottery, SVF and SVV are the subjective values of the fixed and variable options respectively, and γ is the slope of the logistic function, which is a subject-specific parameter. An alternative approach is to use a probit distribution.
Where p is the objective probability (by definition 0.5 for this class of ambiguous lotteries), A is the ambiguity level (the fraction of the total probability that is unknown, 0 for risky lotteries), V is the amount, and α and βare subject-specific risk and ambiguity attitude parameters respectively. One of several alternative approaches is to include ambiguity as an exponential effect8:
Fitting the choice data with the choice function thus provides estimates for the risk attitude (α) and ambiguity attitude (β) for each subject.
6. Analyzing the Neural Data
7. Representative Results
Figure 4 presents the behavioral results of three representative subjects. Each panel presents the choice data and model fit results for one subject under either risk (left) or ambiguity (right). The graphs depict the proportion of trials in which the subject chose the variable lottery as a function of amount, separately for each level of probability or ambiguity. As can be seen, subjects may vary a lot in their attitudes towards risk and ambiguity.
To examine the goodness of the fit, check the r2, which should ideally be over 0.5, and also inspect the curves visually. While all our three example subjects had lawful behavior that enabled reasonable fits, note that subject 2 hardly chose the variable option in the risk condition with the lowest probability (0.13). This suggests that expanding the range of amounts and/or using higher probabilities may provide better results, because it will ensure that subjects choose the variable options on at least some of the trials. Another option is to pre-test each subject on a wide range of amounts and choose those amounts that ensure a comparable number of reference and variable option choices for each individual.
Figure 5 presents the imaging results in one representative subject. Highlighted voxels are ones in which the coefficient of the subjective value predictor under ambiguity (top) or risk (bottom) was significantly different from 0. In this typical subject, significant correlation was found in medial prefrontal cortex (MPFC) and the striatum under both conditions. These areas are the most consistent across subjects, but significant correlations may also be expected in areas in medial and lateral parietal cortex, as well as the amygdala. As activity in this type of tasks is usually weak and noisy you should expect high variability across subjects with many subjects exhibiting significant correlations only in a subset of areas.
Figure 1. Risky and ambiguous stimuli. A) In risky stimuli the red and blue areas of each image on the screen are proportional to the number of red and blue chips in the envelope. Three outcome probabilities were used here: 0.13, 0.25 and 0.38. B) In ambiguous stimuli the central part of the image is obscured with a gray occluder. In the gray area the number of chips of each color is unknown, and thus the probability of drawing a chip of a certain color is not precisely known. Three levels of ambiguity are used here, where 25, 50 or 75% of the image are occluded.
Figure 2. A lottery example. This is an ambiguous lottery, at a 50% ambiguity level. At least 25 of the chips in the envelope are red and at least 25 are blue. If a red chip is drawn the subject will win $18, while they will win nothing if a blue chip is drawn.
Figure 3. The trial structure. A lottery is briefly presented, followed by a delay period. A response cue then prompts subjects to indicate their choice between the lottery on the screen and the reference lottery (in this case a 50% chance of winning $5). Trials are interleaved with long rest periods.
Figure 4. Examples of single subject choice behavior. The graphs present the proportion of trials in which each subject chose the variable option over the reference, as a function of the offered amount, in risky (left) and ambiguous (right) trials. Different curves are for different risk or ambiguity levels. α, risk attitude parameter; β, ambiguity attitude parameter; r2, McFadden's pseudo R-squared, a measure of the goodness of fit of the behavioral model, equivalent to the portion of the variance that is explained by the model; n, number of trials in which response was made (out of a total of 180).
Figure 5. Example of single subject activation maps. Activation maps are presented on a high resolution anatomical image. Highlighted areas are those whose activation was significantly correlated with subjective value under risk (top) or under ambiguity (bottom). In most subjects the medial prefrontal cortex (MPFC) and the striatum represent subjective value under both risk and ambiguity. Corrected p-values are based on a minimum cluster size of 6 functional voxels. Click here to view larger figure.
We have used a method from experimental economics to characterize subjects' behavior and estimate individual attitudes towards risk and ambiguity. We then used these estimates to analyze neural data.
Other methods for examining fMRI activity while subjects make choices under risk and ambiguity have been used before8,12. Our approach, however, combines several important features. First, it uses a parametric design, in which different parameters (amount, probability and ambiguity level) are systematically varied. This allows us to quantify the individual risk and ambiguity attitudes and to compute the subjective value of each option to each subject. Second, having the individual behavioral measure allows us to look for brain areas whose activation is correlated with that measure, separately for risk and ambiguity, at a within subject level. This is a clean way to examine the neural coding of one parameter (subjective value) under different conditions (risk and ambiguity) while controlling for possible differences between those conditions (such as choice behavior). Third, by randomly selecting a trial at the end of the experiment and playing it for real money we encourage subjects to reveal their true preferences13.
At the behavioral level, this method enables us to summarize the unique choice behavior of each subject with only two numbers, representing the risk and ambiguity attitudes of the individual subject. Standard economic theory indicates that for choosers who are behaving consistently these are both necessary and sufficient characterizations of their preferences. Put another way, one can prove that 1) no other possible characterization can be more complete or compact and 2) that all more complex characterizations are redundant. At the neural level, the method allows us to identify the neural representation of the subjective value that individual subjects ascribe to options that they encounter at this necessary and sufficient level of characterization. Of course other characterizations of behavior are possible, but using ad hoc measures of 'riskiness' that cannot be related in a complete way to either the behavior or the neural signals may raise more problems than it solves1.
We described a specific method for localizing areas whose activity is correlated with subjective value. There are other, complementary, ways to analyze the neural data in an exploratory way that does not require prior hypotheses. Clustering methods and Independent Component Analysis (ICA) are such methods that could reveal additional risk- and ambiguity-related activation.
The results revealed substantial behavioral variability across subjects, suggesting several possible extensions of the method that could be used in future studies of risk and ambiguity. First, the methods could be used to probe differences in behavior across individuals, and to identify the neural correlates of those differences, in different subject populations. Of particular interest would be studies of patients hypothesized to exhibit extreme risk-taking behavior, for example those undergoing treatment for drug abuse. Distinguishing between the contributions of risk and ambiguity attitudes to such behaviors and delineating their neural correlates are important for understanding the fundamental causes for such pathological behaviors and for devising behavioral and pharmacological interventions. Other interesting venues would be examining people from different cultures or people of different age groups. The ability to identify specific value-related activity in this way has the potential to reveal group differences that are at the core of observed differences in real life.
Second, the method could be used to examine the influence of specific experiences on the attitudes of individual subjects towards risk and ambiguity. The experimental paradigm could, for example, be employed before and after a behavioral manipulation is conducted or natural events occur, such as an educational intervention, a stress manipulation, or a life-changing event.
Third, a similar paradigm could be used with different ranges of outcomes and probabilities that are appropriate for the question you would like to address. For example, subjects could be presented with choices between different losses, rather than gains, to more directly relate the experimental setting to risk-taking behavior in real life, whose potential outcomes are often negative (e.g. reckless driving or substance abuse). Fourth, non-monetary outcomes could be used to explore attitudes towards risk and ambiguity in different domains, such as food choices and social preferences.
The critical feature of this approach is that it provides a compact and logically complete way to characterize behavior with regard to a fully-specified underlying variable that completely characterizes the preferences of a consistent subject. This thus offers a powerful approach closely tied to theory that moves well beyond ad hoc characterization.
No conflicts of interest declared.
We thank Aldo Rustichini for fruitful discussions and comments on the design.
Funded by NIA grant R01-AG033406 to IL and PWG.
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