2011 by Andrew W. Lo All Rights Reserved

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1 The Evolution o Behavior Andrew W. Lo Course 9.S915: What Is Intelligence? October 7, by Andrew W. Lo

2 Motivation Theory o Economic Behavior Expected Utility Theory Max E[U(C)] s.t. C B C U 0 ( ) > 0, U 00 ( ) < 0 Slide 2

3 Motivation Cognitive and Behavioral Biases Loss Aversion Probability Matching Anchoring Framing Overconidence Overreaction Herding Mental Accounting etc. Slide 3

4 Motivation Urn A Contains 100 Balls: 50 Red, 50 Black Pick A Color, Then Draw A Ball A I You Draw Your Color, $10,000 Prize What Color Would You Preer? How Much Would You Pay To Play? Play? 8/3/ by Andrew W. Slide 4 Lo

5 Motivation Urn B Contains 100 Balls: Proportion Unknown Pick A Color, Then Draw A Ball A I You Draw Your Color, $10,000 Prize What Color Would You Preer? How Much Would You Pay To Play? Play? Knight s s (1921) Dichotomy o Risk vs. Uncertainty o Ininite order Theory o Mind 8/3/ by Andrew W. Slide 5 Lo

6 Loss Aversion A: $240,000 B: $1,000,000 With 25% Probability $0 With 75% Probability ih bbili Which Would You Preer? Slide 6

7 Loss Aversion C: $ 750,000 D: $1,000,000 With 75% Probability $0 With 25% Probability ih bbili Which Would You Preer? Slide 7

8 Loss Aversion A+D: $240,000 With 25% Probability $760,000 With 75% Probability bbl B+C: $250,000 With 25% Probability $750,000 With 75% Probability Now Which Would You Preer? Would Slide 8

9 Probability Matching Consider Repeated Coin Toss Guessing Game: I you re correct, you get $1, otherwise $1 Suppose coin is biased (75% H, 25% T) is Proit maximizing strategy: HHHHHHHHHHHH Actual behavior: HHHTHHHHTTHHHTHHHHTH Common to ants, ish, pigeons, primates, etc. primates etc Why? Is it irrational or adaptive? Slide 9

10 Literature Review Behavorial economics and inance Thaler, Sherin, Statman, Shiller Statman Shiller Psychology and cognitive sciences Simon, Tversky, Kahneman Kh Evolutionary psychology and sociobiology Wilson, Hamilton, Trivers, Cosmides, Tooby, Gigerenzer Evolutionary game theory and economics Malthus, Schumpeter, von Hayek, Maynard Smith, Nowak, Robson, L. Samuelson Behavioral ecology and evolutionary biology Darwin, Levin, Clarke, Slide 10

11 Summary o Brennan and Lo (2011) Our Contribution: Evolutionary Origin o Behavior How did certain behaviors come to be? I they are irrational, why do they persist? Are all behaviors created equal? Simple ramework or answering these questions or answering We derive risk aversion, loss aversion, probability matching, and randomization rom evolution! and Some behaviors are rational rom the population perspective, not rom the individual s i i id l perspective Slide 11

12 Summary o Brennan and Lo (2011) Our Contribution: Evolutionary Origin o Behavior Behavioral biases exist or a reason (hard wired) They may not be advantageous in all environments Understanding their mechanisms is critical or reconciling eicient markets with behavioral inance (Adaptive Markets Hypothesis) Also critical or implementing regulatory reorm implementing regulatory reorm Has implications or intelligence and learning Slide 12

13 Binary Choice Model Consider Asexual Semelparous Individuals Individual lives one period, makes one decision, a or b Generates ospring x = x a or x b, then dies Ospring behaves exactly like parent Individual Behavior: Slide 13

14 Binary Choice Model Consider Asexual Semelparous Individuals I = 1, individual always chooses a (ospring too) I = 0, individual always chooses b (ospring too) I 0 < < 1, individual randomizes with prob. and ospring also randomizes with same Impact o behavior on reproductive success: Summarizes environment and behavioral impact on itnessenvironment and impact Links behavior directly to reproductive success Contains all genetic considerationsall considerations Biological reduced orm Slide 14

15 Binary Choice Model Binary Choice Model Consider Asexual Semelparous Individuals This is repeated over many generations 2011 by Andrew W. Lo 10/7/2011 Slide 15

16 Binary Choice Model Consider Asexual Semelparous Individuals Initial population is uniormly distributed on [0,1] n n n Which behavior dominates? Slide 16

17 Binary Choice Model Consider Asexual Semelparous Individuals Assume is identical across individuals Assume is IID across time Individuals are mindless, not strategic optimizers Which survives over many generations? In other words, what kind o behavior evolves? Evolution is the process o elimination (E. Mayr) l ( Mathematics: ind the that maximizes growth rate This * will be the behavior that survives and lourishes Slide 17

18 Population Arithmetic LLN Slide 18

19 Population Arithmetic Which type o individuals will grow astest? The * that maximizes () on [0,1]: () is strictly concave on [0,1]; unique maximum Three possibilities: () 0 1 Slide 19

20 Population Arithmetic Growth optimal * given by: Slide 20

21 Population Arithmetic How Does * Persist? By Natural Selection: * type takes over exponentially ast Behavior * is optimal or the population the population Behavior * is not necessarily optimal or the individual This requires no intention, deliberation, or intelligence Contrast this behavior with utility maximization! Slide 21

22 Probability Matching Explained Consider Special Case For : Outcomes x a and x b are perectly out o phase Probability matching! This behavior will dominate the population (eventually) Slide 22

23 Probability Matching Explained What About the Optimal Strategy or the Individual? ˆ Suppose p > ½ ; then = 1 The irst time x a = 0, all individuals o this type vanish This behavior cannot persist; * persists * may be interpreted as a primitive version o altruism as a primitive version o altruism When Is Probability Matching Advantageous? g When two choices are highly negatively correlated Diversiication improves likelihood o survival improves o survival Nature Abhors An Undiversiied Bet Slide 23

24 Probability Matching Explained Consider A Simple Ecology with Rain/Shine: Decision: build nest in a or b? i ild i b? Optimize or randomize? a: 1 b: Slide 24

25 Probability Matching Explained Generation = 0.20 = 0.50 *= 0.75 = 0.90 = ,020 2, ,766 7, , ,292 65, , , , , , ,771,470, , ,314, , ,943, ,954 1, , ,122 3, , , , , ,171 22, ,648 1,787,613 61, ,469 4,020, , ,022 9,047, , ,213 6,786,657 1,215, ,306 15,272, , ,429 34,366, , ,019 77,323,623 2,667, , ,996,290 7,203,495 0 p = m = 3 Slide 25

26 Probability Matching Explained Now Consider a More General Then the growth optimal behavior * depends only on Slide 26

27 Probability Matching Explained Growth optimal behavior * given by: Slide 27

28 Probability Matching Explained Exact probability matching condition: condition: Slide 28

29 Risk Preerences To Study Risk Preerences, Let b Be Riskless Parametrize b as a convex combination o a outcomes Slide 29

30 Risk Preerences Growth optimal behavior *: Always choose risky option a Randomize choice with probability Always choose sae option b b Slide 30

31 Risk Preerences Growth optimal behavior *: p = 1/3 For s 1, choice is deterministic, but not when s >> 1 Slide 31

32 Risk Aversion Deine risky outcomes relative to riskless outcome Suppose p p = ½ and * = ½ (indierent between a= ½ a and b) Slide 32

33 Risk Aversion can be viewed as an evolutionary risk premium Due to Jensen s Inequality: Risk aversion is hard wired into survivors Equilibrium is not necessary to determine Slide 33

34 Loss Aversion Two Key Observations: 1. Must translate ecundity into inancial wealth 2. Total wealth is what matters, not increments Deine a reproduction unction c(w) that maps inancial wealth w into number o ospring c(w): Slide 34

35 Loss Aversion Slide 35

36 Loss Aversion But What About the Reerence Point? Has to do with incremental vs. absolute reward Experimenter oers incremental payo Preerences shaped by absolute payo (x) Explains why experiments yield inconsisent indings yield inconsisent For simplicity, suppose c(w) = w Always choose risky option a Randomize choice with probability Always choose sae option b Slide 36

37 Systematic vs. Idiosyncratic Risk Natural Selection Yields The Following Behaviors: Probability matching ( Herrnstein s Law ) Randomization Risk aversion and risk sensitive oraging behavior Loss aversion, anchoring, raming anchoring What I (x a,x b ) Are Not Identical Across Individuals? Suppose ecundity is IID across individuals and time Slide 37

38 Systematic vs. Idiosyncratic Risk Non stochastic! Slide 38

39 Systematic vs. Idiosyncratic Risk Growth Optimal Behavior With Idiosyncratic Risk: In this case, no dierence between individually optimal and growth optimal behavior No behavioral biases ; no risk aversion; everyone behaves rationally (Homo economicus) Behavior can be identical because environment is not I environment is identical, behavior cannot be is identical cannot Nature abhors an undiversiied bet! Slide 39

40 Bounded Rationality and Intelligence Simon s Notion o Satisicing : Heuristics, not optimization Develop mental models to simpliy decisions models to simpliy decisions Impact on AI, but not on economics How do we know what is good enough? Answer We Don t! Our Heuristics Evolve In our ramework, let state variable z z be correlated to x and observable at some cost c 10/7/ by Andrew W. Lo Slide 40

41 Bounded Rationality and Intelligence Consider Getting Dressed: 5 Jackets, 10 Pants, 20 Ties, 10 Shirts, 10 Pairs o Pairs Socks, 4 Pairs o Shoes, 5 Belts Possible 2,000,000 Possible Outits! Takes 1 Second To Evaluate Each Outit How Long To Get Dressed? 23.1 Days! How Do We Get Dressed So Quickly? Evolution o Heuristicso 10/7/ by Andrew W. Lo Slide 41

42 Bounded Rationality and Intelligence What Is Intelligence? An Evolutionary Deinition: Behavior that coners reproductive advantage reproductive advantage Hawkins memory/prediction model its this deinition What Is Stupidity? Behavior that is counterproductive to survival is to survival 10/7/ by Andrew W. Lo Slide 42

43 Bounded Rationality and Intelligence Evolution At The Speed o Thought Behavioral plasticity Hierarchy o behaviors (Herrnstein vs. Heimlich) Implications or neurophysiology p Slide 43

44 Other Extensions Sexual reproduction Iteroparity Multivariate multi stage choice problems Resource constraints, strategic interactions, population equilibrium p Time varying and nonstationary (x a,x b ) Environmental shocks yield punctuated equilibria equilibria Group selection Complex adaptive systems Slide 44

45 The Challenge Can We Construct a Complete TheoryoHuman Theory o Human Behavior? Slide 45

46 The Challenge Consilience (E.O. Wilson, 1998): The Consilience o Inductions takes place when an Induction, obtained rom one class o acts, coincides with an Induction, obtained rom another dierent class. This Consilience is a test o the truth o the Theory in which it occurs. WilliamWhewell, 1840, Philosophy o the Inductive Sciences, o 48

47 The Challenge Framework or modeling the evolution o behavior Abstracts rom underlying genetics Biological reduced orm model Simplicity implies behaviors are primitive and ancient Mathematical basis o the Adaptive Markets Hypothesis Markets Evolution determines individual behavior Evolution also determines aggregate dynamics l d Eiciency and irrationality are both adaptive The key is how environment is related to behavior Slide 47

48 The Challenge Instead o: It s the economy stupid! We Should Say: Say: It s s the environment, stupid! environment stupid! Slide 48

49 Thank You!

50 Motivation Preerences Under Certainty: Non Satiation Transitivity Completeness Diminishing Marginal Utility Finance Theory Is Complete Page 50

51 Motivation Preerences Under Uncertainty: Utility o a random variable Diicult to evaluateto Requires strong assumptions Von Neumann and Morganstern Expected Utility Theory (EUT) Modern Economics and Finance Are Built on EUT on EUT Page 51

52 Motivation G2 and G3: G3: Probability G1 G2 G3 50% $50,000 $50,000??? 50% ($10,000)??? ($10,000) Certainty X1 X2 X3 Equivalent:????????? Page 52

53 Motivation Estimated Utility Function $20,000 -$10,000 $0 $10,000 $20,000 $30,000 $40,000 $50,000 $60,000 Page 53

54 Motivation Denote By U(x) Your Utility Function U($50,000) = 1, U( $10,000) = 0 Consider three gambles, G1, G2, G3:,, G1: $50,000 With 50% Probability bbl $10,000 With 50% Probability What is the most th t you would pay or G1? Page 54