Frontiers in Social Neuroscience and Neuroeconomics: Decision Making under Uncertainty. September 18, 2008

Transcription

1 Frontiers in Social Neuroscience and Neuroeconomics: Decision Making under Uncertainty Kerstin Preuschoff Adrian Bruhin September 18, 2008

2 Risk Risk Taking in Economics Neural Correlates of Prospect Theory Individual Heterogeneity Open Questions Ambiguity α-maxmin-model Individual Heterogeneity Open Questions References

3 Decision Making under Risk

4 Decisions under Risk The decision maker knows all possible outcomes and the associated probabilities of realization. However, ex ante she does not know which outcome will be realized. Risky lotteries are easily tractable but rare in real life. Examples: Games of hazard (betting on dice, roulette, etc.). (Speculating on rising/falling prices of highly liquid assets.)

5 Expected Utility Theory (EUT) EUT is the standard model for decision making under risk (Bernoulli, 1738; von Neumann and Morgenstern, 1944). In EUT, an individual with utility function u(x) values the binary lottery G with outcomes x 1 and x 2 by its expected utility, E [u (G)] = u (x 1 ) p + u (x 2 ) (1 p), where p denotes the probability that x 1 is realized.

6 Expected Utility Theory (EUT) If u(x) is concave, the lottery s expected utility, E [u (G)], is smaller than its expected value s utility, u (E [G]), and the individual is said to be risk averse. u(x 1 ) u(e[g]) u(x 2 ) x 2 E[G] x 1 x

7 Expected Utility Theory (EUT) If u(x) is concave, the lottery s expected utility, E [u (G)], is smaller than its expected value s utility, u (E [G]), and the individual is said to be risk averse. u(x 1 ) u(e[g]) E[u(G)] u(x 2 ) x 2 E[G] x 1 x

8 Expected Utility Theory (EUT) If u(x) is concave, the lottery s expected utility, E [u (G)], is smaller than its expected value s utility, u (E [G]), and the individual is said to be risk averse. u(x 1 ) u(e[g]) E[u(G)] u(x 2 ) Risk Premium RP=E[G] ce x 2 ce E[G] x 1 x

9 Measuring Risk Aversion The Relative Risk Premium, RRP, is a convenient descriptive measure of risk aversion as its calculation only requires the expected outcome, E(G), and the certainty equivalent, ce: RRP = E (G) ce E (G) If RRP > 0 an individual is risk averse. (EUT: u (x) < 0)... RRP = 0 an individual is risk neutral. (EUT: u (x) = 0)... RRP < 0 an individual is risk seeking. (EUT: u (x) > 0)

10 EUT Fails as Descriptive Model 25 years of experimental research have demonstrated that people often do not behave as expected utility theory (EUT) predicts. (Hey and Orme, 1994) Gain Domain Loss Domain RRP RRP p p

11 Prospect Theory (PT) PT (Kahneman and Tversky, 1979) is based on the notion of diminishing sensitivity. In PT, a binary lottery s value is given by v(g) = v(x 1 )w(p) + v(x 2 )[1 w(p)], x 1 > x 2. v(x) 0 w(p) x p

12 Prospect Theory (PT) In contrast to EUT, risk aversion is driven by both the curvature of the value function, v(x), and the non-linearity in probability weighting, w(p). PT describes the fourfold pattern of risk attitudes. For aggregate choices, PT is one of the best descriptive models for individual decision making under risk. Diminishing sensitivity and potential neural representations of v(x) and w(p) add explicative power to PT.

13 Potential Neural Correlates of PT v(x) : VMPFC and ventral striatum are regions most consistently associated with decision utility. (Tom et al., 2007; Plassmann et al., 2007; Knutson et al., 2007) w(p) : Several brain regions exhibit inversely S-shaped activation patterns with respect to probability changes. Causality? (Berns et al., 2007; Paulus & Frank, 2006) ACC may integrate the value and probability weighting function. (Berns et al., 2007) Possible temporal separation of v(x) and w(p) in dopaminoreceptive structures. (Preuschoff et al., 2006)

14 Heterogeneity in Risk Taking Behavior Generally, there is vast individual heterogeneity and EUT may still be valid for a minority of subjects. Individual heterogeneity is crucial in economics as even small minorities can have decisive impacts on the outcomes in imperfect markets (especially under strategic complementarity). (Fehr & Tyran, 2005; Haltiwanger & Waldman, 1985, 1989) Are there distinctly different behavioral types when it comes to decision making under risk?

15 Behaviorally Identifying Risk Taking Types Endogenous classification of individuals by finite mixture models robustly identifies 20% EUT- and 80% PT-types. (Bruhin et al., 2007; Conte et al., 2008) Gain Domain Loss Domain w(p) EUT Types PT Types w(p) EUT Types PT Types p p

16 Outlook Open Questions Behavioral classification in EUT- and PT-types may help to identify (the) neural representation(s) of the probability weighting function, w(p): Are there differences in neural activity (in the rdlpfc?) between EUT- and PT-types? Causality: Do EUT-types become irrational when their rdlpfc is down regulated by TMS? Is there a genotype for EUT and PT?

17 Decision Making under Ambiguity

18 Decisions under Ambiguity The decision maker knows all possible outcomes but has only incomplete knowledge about the associated probabilities of realization. Examples: Submitting a paper to a journal. Participating in a job interview.

19 α-maxmin-model In the α-maxmin-model (Ghirardato et al., 2004) an ambiguous lottery s value is given as weighted average between the expected utilities of the worst and best possible scenario: αmeu (G) = α [u (x 1 ) p min + u (x 2 ) (1 p min )] + (1 α) [u (x 1 ) p max + u (x 2 ) (1 p max )]

20 α-maxmin-model In the α-maxmin-model (Ghirardato et al., 2004) an ambiguous lottery s value is given as weighted average between the expected utilities of the worst and best possible scenario: αmeu (G) = α [u (x 1 ) p min + u (x 2 ) (1 p min )] + (1 α) [u (x 1 ) p max + u (x 2 ) (1 p max )] If α > 0.5 the decision maker is ambiguity averse.... α = 0.5 the decision maker is ambiguity neutral.... α < 0.5 the decision maker is ambiguity seeking.

21 Individual Heterogeneity: Preliminary Results First results from a finite mixture estimation indicate two behavioral types: About 40% of the subjects behave on average neutrally towards ambiguity (α 0.5). About 60% of the subjects are on average ambiguity averse (α 0.8). However, results are very preliminary and the used data set is not optimal: Only simple lotteries without variation in outcome differences. Binary choices instead of certainty equivalents.

22 Outlook Open Questions After estimating a finite mixture model for the α-maxminmodel: Do behavioral types correlate across the domains of risk and ambiguity? In individual classification? Neurally? (Are similar neural circuits involved in making risky and ambiguous decisions?) Are there differences in neural activity between distinct ambiguity types?

23 References Bernoulli D. (1738/1954), Exposition of a New Theory on the Measurement of Risk, Econometrica, 22, Berns G.S., C.M. Capra, J. Chappelow, et. al. (2007), Nonlinear Neurobiological Probability Weighting Functions for Aversive Outcomes, Neuroimage, 39, Bruhin A., H. Fehr-Duda, T. Epper (2007), Risk and Rationality: Uncovering Heterogeneity in Probability Distortion, SOI Working Paper No. 0705, University of Zurich. Conte A., J. Hey, P. Moffat (2008), Mixture Models of Choice under Risk, Journal of Econometrics, forthcoming.

24 References Fehr E., J.R. Tyran (2005), Individual Irrationality and Aggregate Outcomes, Journal of Economic Perspectives, 19, Ghirardato P., F. Maccheroni, M. Marinacci (2004), Differentiating Ambiguity and Ambiguity Attitude, Journal of Economic Theory, 118, Haltiwanger J.C., M. Waldman (1985), Rational Expectations and the Limits of Rationality: An Analysis of Heterogeneity, American Economic Review, 75, Haltiwanger J.C., M. Waldman (1989), Limited Rationality and Strategic Complements: The Implications for Macroeconomics, Quarterly Journal of Economics, 104,

25 References Hey J., C. Orme (1994), Investigating Generalizations of Expected Utility Theory Using Experimental Data, Econometrica, 62, Kahneman D., A. Tversky (1979), Prospect Theory: An Analysis of Decision under Risk, Econometrica, 47, Knutson B., S. Rick, G.E. Wimmer, et. al. (2007), Neural Predictors of Purchases, Neuron, 53, Paulus M.P., L.R. Frank (2006), Anterior Cingulate Activity Modulates Nonlinear Decision Weight Function of Uncertain Prospects, Neuroimage, 30,

26 References Plassmann H., J. ODoherty, A. Rangel (2007), Orbitofrontal Cortex Encodes Willingness to Pay in Everyday Economic Transactions, Journal of Neuroscience, 27, Preuschoff K., P. Bossaerts, S.R. Quartz (2006), Neural Differentiation of Expected Reward and Risk in Human Subcortical Structures, Neuron, 51, Tom S., C. Fox, C. Trepel, R. Poldrack (2007), The Neural Basis of Loss Aversion in Decision-Making Under Risk, Science, 315, von Neumann J., Morgenstern, O. (1944), The Theory of Games and Economic Behavior, 1st edn. Princeton.