Behavioural Economics Flashcards
(188 cards)
1
Q
Topic 3.1 L - What is expected utility theory?
A
a Normative model of rational choice that has dominated most of economic analysis as the standard theory of choice under uncertainty risk. It is assumed that all reasonable people obey the axioms most of the time. It is worth noting that in several choice problems, it has been observed that preferences systematically violate the axioms.
2
Q
Topic 3.1 L - What is a prospect (with formula)?
A
A prospect denoted by (x1,p1, … ; xn,pn), is a contract that yields outcome xi with probability pu where p1 + p2 + … + pn = 1.
We omit null outcomes and use (x, p) to denote the prospect (x, p; 0, 1 - p) that yields x with probability p and 0 with probability 1 - p.
A riskless prospect that yields x with certainty is denoted by (x).
3
Q
Topic 3.1 L - What words are analogous to prospect?
A
Lottery and game.
4
Q
Topic 3.1 L - Expected Value (EV) of a prospect?
A
The value of each possible outcome * the probability of that outcome.
5
Q
Topic 3.1 L - What can be deduced about expected values and utilities and the preference of individuals?
A
People seek to maximise expected utility, not expected value.
6
Q
Topic 3.1 L - Expected Utility formula?
A
E(u) = p1 * o1 + … + Pn * On.
The utility of each outcome multiplied by the probability of each outcome.
7
Q
Topic 3.1 L - What is the difference between EV and EU?
A
Expected Value is the probability weighted average of the monetary value.
Expected Utility is the probability weighted average of the utility from the potential monetary values.
8
Q
Topic 3.1 L - How do endowments play into expected utility?
A
Utility will be derived from the current endowment + the utility from the gain or loss. ‘w’ is the current endowment.
9
Q
Topic 3.1 L - Expected Utility Theory: What are the three tenets that relies on?
A
- Expectations.
- Asset Integration.
- Risk Aversion
10
Q
Topic 3.1 L - Expected Utility Theory - Expectations?
A
The overall utility of a prospect, denoted by U, is the expected utility of its outcomes.
People choose the risky item which yields a higher expected utility than others.
U(x1; p1; … ; xn; pn) = p1u(x1) + p2u(x2) + … + pnu(xn)
11
Q
Topic 3.1 L - Expected Utility Theory - Asset Integration?
A
A prospect is acceptable if
the utility resulting from integrating the prospect with
one’s assets exceeds the utility of those assets alone.
(x1; p1; … ; xn; pn) is acceptable at asset position w if
U(w + x1; p1; … ;w + xn, pn) > u(w)
12
Q
Topic 3.1 L - Expected Utility Theory - Risk Aversion?
A
u is concave (u’’ < 0).
13
Q
Topic 3.1 L - Risk Aversion?
A
A preference set that results in E(U) < E(V). The degree of risk aversion is represented by the concavity of the utility function of an individual.
14
Q
Topic 3.1 L - What can be said about someone who is risk neutral?
A
They have a constant marginal utility of wealth, hence , a utility function linear in wealth. Maximising expected value is the same as maximising the expected utility.
15
Q
Topic 3.1 L - How will marginal utility change for a risk loving person?
A
A risk loving person will have a convex utility function has increasing marginal utility of wealth. Each additional dollar provides greater additional happiness that the dollar before it.
16
Q
Topic 3.1 L - What can the Expected Utility theory be called? What is some information about this name?
A
The con Neumann-Morgenstern (vNM) utility. They characterised the 4 expected utility axioms: completeness, transitivity, continuity and independence.
17
Q
Topic 3.1 L - Continuity Definition?
A
Very small changes in probabilities do not change the preference ordering between lotteries.
18
Q
Topic 3.1 L - Independence Definition?
A
If we mix two lotteries with a third one, the preference ordering of the two pictures will not change and is independent of the particular third lottery used.
19
Q
Topic 3.1 L - What is Independence sometimes called and what is the requirement?
A
The substitution axiom.
Independence requires that pA + (1 - p)C > pB + (1 - p)C
20
Q
Topic 3.1 L - Who originally described the pattern of violation in EUT in which:
B > A then it should be that D > C
In practice, most people answer B > A and C > D? What principle is violated in particular?
A
The Allais Paradox. It is a model that works on utility. The principle of EUT that is violated is the Expectation Principle.
21
Q
Topic 3.1 L - Explain the Certainty Effect?
A
AKA the Allais paradox. People overnight outcomes that are considered certain relative to outcomes which are merely probable.
22
Q
Topic 3.1 L - What is implied by the reflection effect? Intuitive understanding?
A
Risk aversion in the positive domain and risk seeking in the negative domain.
“Overweighting of certainty” favours risk aversion in the domain of gains and risk seeking in the domain of losses.
In the positive domain, the certainty effect contributes to a risk averse preference for a sure gain over a larger gain that is merely probable.
In the negative domain, the same effect leads to a risk seeking preference for a loss that is merely probable over a smaller loss that is certain.
23
Q
Topic 3.1 L - The Asian Disease Example?
A
An example by Tversky and Kahneman (1981) in which the same question was asked to doctors (with statistical knowledge) but from the perspective of the gains in life and the losses of life. One choice has certainty of death/ life and the other had a framing effect of a probability of death/ life. Despite the outcomes being identical, When preventing deaths, the doctors chose the chance of saving deaths(the probability), whereas when framed in terms of how many people will live, the majority changed to picking the certainty option.
24
Q
Topic 3.1 L - What is the Major Difference between Prospect Theory and Expected Utility Theory?
A
Prospect Theory is the reference-dependence with loss aversion. With EUS, we need to know the state of wealth. In Prospect theory, you also need to know the reference state. Kahneman and Tversky introduced prospect theory in 1979.
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Topic 3.2 L - Why was prospect theory formalised?
To accommodate systematic violations of the standard expected utility theory.
26
Topic 3.2 L - What is the symbol used for the overall value of an edited prospected, what is it expressed in terms of?
V.
| It is expressed in terms of two scales, v and π
27
Topic 3.2 L - Prospect Theory: first scale, v?
The first scale, v, assigns to each outcome x a number. v(x), which reflects the subjective value of that outcome. Outcomes are described relative to a reference point, which serves as the zero point of the value scale.
28
Topic 3.2 L - Prospect Theory: The second scale, π?
The second scale, π, associates with each probability p a decision weight π(p), which reflects the impact of p on the overall value of the prospect.
29
Topic 3.2 L - For prospects of the form (x, p; y, q), when would the prospect be strictly positive?
if x,y > 0 and p + q = 1.
| So if all outcomes are strictly positive
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Topic 3.2 L - For prospects of the form (x, p; y, q), when would the prospect be strictly negative?
If all outcomes are negative. x,y < 0 and p,q = 1
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Topic 3.2 L - For prospects of the form (x, p; y, q), when would the prospect be regular?
If it is neither strictly positive nor strictly negative. So either p + q < 1 or X ≥ 0 ≥ y or x ≤ 0 ≤ y (so either one of the payoffs (y,x) is positive and one is negative.
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Topic 3.2 L -
Finish SLIDE 7
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Topic 3.2 L - For Regular Prospects, V is defined on prospects, while v is defined on outcomes. When would the two concede? (formula)
V(x,1) = V(x) = v(x)
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Topic 3.2 L - How can we generalise the expected utility theory by relaxing the expectation principle for a regular prospect? (Formula and values). What is this known as (slide title)?
V(x,p; y,q)= π(p)v(x) + π(q)v(y)
Where v(0) = 0, π(0) = 0 and π(1) = 1
Known as the general form for regular prospects.
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Topic 3.2 L - General Form for Strictly positive and strictly negative prospects: What is the process and explain?
These prospects are separated into two components:
1. The Risk-less Component i.e. the minimum gain or loss which is certain to be obtained or paid.
2. The Risky Component i.e. the additional gain or loss which is actually at stake.
For example, (400; 0:25; 100; 0:75) is naturally decomposed into a sure gain of 100 and the risky prospect (300, 0.25).
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Topic 3.2 L - General Form for Strictly positive and strictly negative prospects: What is the equation for strictly positive and strictly negative prospects? How would you explain this equation? Example?
If p + q = 1 and either
a) x > y > 0 [Strictly positive] or
b) x < y < 0 [Strictly Negative], then
V (x,p; y, q) = v(y) + π(p)[v(x) - v(y)]
The decision weight is applied to the value-different [v(x) - v(y)], representing the risky component of the prospect. v(y) is the risk-less component.
V (400, .25; 100; .75) = v(100) + π(.25)[v(400) - v(100)]
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Topic 3.2 L - What are the main elements of prospect theory?
1. Reference Points
2. Diminishing Marginal Sensitivity.
3. Loss-Aversion
4. Decision-Weighting.
These general forms represent all of these.
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Topic 3.2 L - Prospect Theory Elements: 1. Reference Points?
Changes are measured relative to reference points, serving as a zero point of the value scale (has a 0 value).
The carriers of value are changes in wealth or welfare, rather than final states.
"v" measures the value of deviations from the reference point.
EXTRA: We often assume that the relevant reference point of evaluating gains and losses is the current status of wealth or welfare, but the reference point may be the outcome that you expect or feel entitled to.
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Topic 3.2 L - Value Functions in Prospect Theory: What would be the y-axis and x-axis?
Y-Axis: Value
| X-Axis: Gains/ Losses.
40
Topic 3.2 L -Prospect Theory Elements: 1. Diminishing Marginal Sensitivity? How would we prove this theory?
The value function for changes of wealth is concave above the reference point (v''(x) < 0, for x > 0) and convex below the reference point (v''(x) > 0, for x <0). This can be proved through the following scenario:
Prospects (6000; .25) <18%> or (4000; .25; 2000; .25) <82%>
vs
Prospects (-6000; .25) <70%> or (-4000; .25;-2000; .25) <30%>
The frequency of responses to a study is show with percentages within <>.
We can see that people tend to take the more risky option with losses and less risky option with gains. This example is meant to show diminishing marginal sensitivity though?
41
Topic 3.2 L - Prospect Theory Elements: 3. Loss Aversion? What conclusion can we make?
Pleasure of gaining money is less than the pain of losing money, so symmetrical bets of an equal chance winning 50 an equal chance of the losing 50 are unattractive.
Moreover, there is an aversiveness of symmetry bets when the stake increases [for x>y≥0 , (y, .5; -y, .5) is preferred to (x, .5; -x,.5]
We conclude that v(x) < -v(-x) for x > 0 and
the value function for losses:
v'(x) < v'(-x)
[value is lost at a greater rate than a the same and opposite change in gains]
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Topic 3.2 L - Prospect Theory Elements: 3. Loss Aversion - How would you measure the extent of loss aversion and what is the typical gain that would be required to offset the chance of a loss.
What is the smallest gain that is needed to balance an equal change to lose, say £100?
The typical answer is £200, but the LOSS AVERSION RATION typically has a range between 1.5 and 2.5
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Topic 3.2 L - Prospect Theory Elements: 3. Loss Aversion - What are the implications (2 effects)?
The Endowment Effect: The difference between what potential buyers are wiling to pay (WTP) for goods and what potential sellers are willing to accept (WTA) for the same goods.
The Disposition Effect: Investors tend to hold on to stocks that have lost value (relative to their purchase price) too long, while being eager to sell stocks that have risen in price.
44
Topic 3.2 L - Value Functions: What properties describe the most commonly used value function?
v(x) = { x^α. If x ≥ 0
{ -𝛌(-x)^β If x < 0
```
Where
α: coefficient of diminishing marginal sensitivity for gains.
β: coefficient of DMS for losses.
𝛌: coefficient of loss-aversion
x: gain/loss
```
45
Topic 3.2 L - Value Function: Why does an individuals preference to integrate or segregate gains and losses matter?
Due to the value function being concave in the domain for gains and convex in the domain for losses, it matters how outcomes are bundled.
Gains and losses can be segregated or Integrated.
Integrated: You have gained a total of £75, translating to v(75) in value terms.
Segregated: You have won £25 and then £50, translating in value terms to v(25) + v(50)
46
Topic 3.2 L - Value Functions: What would the implications be for the following game:
You buy two lottery tickets at a charity event, and you win £25 on the first and £50 on the second. How does prospect theory differ to the standard theory?
Think of the implications of each and how it each would look on a graph.
a) Integrated: You have gained a total of £75, translating to v(75) in value terms.
b) Segregated: You have won £25 and then £50, translating in value terms to v(25) + v(50)
According to standard theory, no matter how you describe the various outcomes, you end up with an additional £75. PT said that BUNDLING MATTERS.
People value two gains more when they are segregated than when they are integrated.
See Brainscape Assistant. 1.
47
Topic 3.2 L - Prospect Theory 4 - Decision Weighting: How does weighting effect outcome? What is the formula and how does it differ?
The value of each outcome is multiple by a decision weight.
V(prospect) = π(p)v(x) + π(q)v(y)
NOT
pv(x) + qv(y)
Decision weights [π(p,q)] measure the impact of events on the desirability of prospects, not merely the perceived likelihood of these events.
48
Topic 3.2 L - Prospect Theory 4 - Decision Weighting:: When does the perceived likelihood and decision weights value coincide. What is an important distinction between the two?
If π(p) = p. If the expectation principle holds.
Decision weights are not probabilities so do not obey probability axioms.
49
Topic 3.2 L - What are the first 3 main properties of the decision weighting function?
1. π(0) = 0 and π(1)=1
2. π is an increasing function of p, which means that the value of π increases as the probability increases.
3. Very low probabilities are generally overweighted, that is, π(p) > p for small p. [but, THIS IS NOT THE SAME AS OVERESTIMATION - overestimation regress to the wrong assessment of the probability of rare events]
50
Topic 3.2 L - What is fourth main property of the decision weighting function? (function required)
Subcertainty
π(p) + π(1-p) < 1 for all p not equal to 1
[so not just for small p]
See Brainscape Assistant 2.
51
Topic 3.2 L - What are the implications of subcertainty?
Hint:
slope
preferences
The slope of π can be viewed as a measure of the sensitivity of preferences to changes in probability.
It shows that preferences are generally less sensitive to variations of probability than the expectation principle would dictate.
It therefore captures peoples attitudes to uncertain events. Namely, that the sum of the weights associated with complementary events is typically less than the weight associated with the certain event. People are limited in their ability to comprehend and evaluate extreme probabilities.
52
Topic 3.2 L - Recap, what is the difference, in terms of the formula, for EUT and PT?
Graph?
EUT sets the EU subject to the probability of the outcome and the utility of achieving it.
PT sets a probability weighting function, and instead of the utility, looks at the value of the potential outcome.
For low probabilities, π(x) < x and for high probability π(x) > x.
See Brainscape Companion 3 for the graph.
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Topic 3.2 L - Closing remarks on weighting functions?
People are limited in their ability to comprehend and evaluate extreme probabilities.
Highly unlikely events are either ignored or overweighted, and the difference between high probability and certainty is
either neglected or exaggerated.
Consequently, is not well-behaved near the end-points.
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Topic 3.2 L - Estimations: Parameters for Prospect Theory - What was the estimated model?
See Brainscape Assistant 4.
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Topic 3.2 L - Decision Wieghts: What can be concluded from the proposed theory of Kahneman and Tversky as well as the estimate results for p*?
The is a p* such that:
1. π(p) > p and concave if p < p*
2. π(p) < p and convex if p > p*
p8* is generally observed to be less than 0.5. People overstate small probability and understate high probabilities.
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```
Topic 3.2 L - Summary of EUT and PT?
Hint:
Basis Objects
Risk Aversion
Loss aversion
Probability Estimation
Problem Descriptions
```
EUT:
1. The basic objects of preferenences are states of wealth (including non-monetary resources like health care).
2. The utility function is risk averse everywhere.
3. Loss aversion cannot be defined as EUT does not identifiy a status quo.
4. People evaluate probabilities linearly.
5. Problem descriptions have no effect as long as the problem is logically the same.
PT:
1. The basic objects of preferences are changes from a neutral reference point (gains and losses)
2. The value function is risk averse for gains and risk seeking for losses.
3. The value function implies loss aversion.
4. People evaluate probabilities nonlinearly.
5. Problem descriptions can change the reference level; hence the definition of gains and losses can change.
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Topic 3.2 L - PT: Probabilistic Insurance?
Two Options:
A) Pay a premium for full coverage.
B) Pay half a premium for coverage on half the days of a year.
Normative theory would suggest that, due to a concave utility function, most people reject B.
P to P/2 is a smaller loss than p/2 to 0 (the certainty effect)
Framing an insurance premium as giving full protection against specific risks makes it more attractive.
58
Topic 3.2 L - Two Effects highlighted by deal or no deal? Application to EUT?
Break Even Effect: Risk aversion seems to decrease after earlier expectations have been shattered by opening high-value briefcases. (similar to horse racers betting on long shots before they go home to break even.
House-Money Effect: Risk aversion decreases after earlier expectations have been surpassed by opening low-value briefcases. Forecasts that investors are more prone to buy higher risk stocks after a profitable trade.
EUT does not predict this as preferences are assumed to be constant, irrespective of the auth travelled before arriving at the problem.
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Topic 3.2 L - Complete After Exam slide 41 -44.
*
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Topic 1.1 - Relationships with regards to preferences and notation?
Preferences are based on relationships. e.g. a being weakly or strongly preferred to b.
Capital letters are used to denote relations.
Lower case letters are used to denote entities.
e.g. Betsy is younger than Alfred: bRa.
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Topic 1.1 - Universe meaning?
Used to reference what domain we are working in when picking entities.
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```
Topic 1.1 -
1. ≥?
2. >
3. ~
Link in with universe and state what sort of relation this is.
```
1. "at least as good as"
2. "strictly better than"
3. Indifference between two options.
4. >
5.
We state that x,y can be compared as part of universe Z.
A relation between the two would be a binary relation.
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Topic 1.1 - What is a rational preference relation?
```
One that is transitive (consistency between ranking: A>B & B>C, so A>C)
and complete (for all x,y in Z, we have a preference and can thus rank x and y.
```
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Topic 1.1 - Representation Theorem?
If the universe is finite and a relation (e.g. >) is complete and transitive, there exists a utility function representing the relation.
so x > y --- u(x) > u(y).
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Topic 1.1 - What is the consumption set?
The domain of all possible bundles within a universe.
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Topic 1.1 - What are the presumptions required for rational choices to be made?
(2)
1. Rational preference ordering.
| 2. When faced with a consumption set, the most preferred item (or one of the preferred items when there is a tie).
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Topic 1.1 - What is the Budget set formula and the MRSx,y associated with it?
See Brainscape Note 5
| MRS = p(x) / p(y)
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Topic 1.1 - Who identified choice as more fundamental than preference and why?
Samuelson (1938) identified choice as more fundamental than preference as choice is observed.
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Topic 1.1 - Notation: an agents choice rule over a many A in terms of x and y.
See Brainscape Assistant 6.
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Topic 1.1 - When is a choice rule rationalizable?
A choice rule is rationalizable if there exists a preference set that maximises
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Topic 1.1 - How would we test rationalizability looking at choice date?
WARP: the Weak Axiom of Revealed Preferences. This would enable us to create a complete and transitive understanding of an individuals preferences based on their previous choices. It is based on the notion that if the prices of goods stay the same, the individual will not deviate from their choice unless the benefits of another option increased.
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Topic 1.1 - Rule for WARP?
if x,y ε A n B, x ε C(A) and y ε C(B), then x ε C(B)
Or, with single-valued choice rules:
if x,y ε A n B, and x = C(A), then it is not the case that y = C(B)
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Topic 1.1 - Sunk Costs? It's relation to Economic Theory?
Costs beyond recovery at the time when the decision is made.
| ET implies that only incremental costs and benefits should affect decisions, not historical costs.
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Topic 1.2 - Basketball Game?
Highlights the sunk costs fallacy
Proposed by Thaler in 1980. a) You pay £80 for a ticket but cannot attend on the day due to a snow storm.
b) You get gifted the ticket but cannot attend.
75
Topic 1.2 - Calculator/ Jacket Example?
Proposed by Kahneman and Tversky in 29184.
You buy a jacket for $125 (x) and a calculator for $15 (y) from two separate stores, 10 minutes away. A flash sale reduces the price of the calculator or jacket by $5. Do you go to get the discount on the jacket, what about the calculator? You learn both items are out of stock, so must travel to another store but will attain a $5 discount (z). The study showed that x y > z, x > z but x~y
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Topic 1.2 - What is the opportunity costs equilibrium in standard theory?
Marginal cost = marginal benefit.
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Topic 1.2 - How does the Jacket/ Calculator highlight issues with the standard economic model?
It highlights the opportunity cost being inconsistent. In both occasions, a saving of $5 would be made for a 10 minute trip, but based on the scenario, the preferences of the individual change.
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Topic 1.2 - opportunity cost?
The benefit forgone of the next best alternative.
Alternative: a1, a2, ..., an
Utilities: u(a1), u(a2),...,u(an)
Opportunity cost:
C(ai) = max[u(a1), u(a2),...,u(an)]
E.g the opportunity cost is the maximum utility attainable through the other acts.
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Topic 1.2 - Menu Dependence defintion?
When preferences are altered by the menu.
Violates the following: If c(A) = {x} from menu {x,y} and you are not indifferent between {x,y}, you must not chose y from menu {x,y,z}.
Think of the economist example.
80
Topic 1.2 - What effect does the economist example show?
The decoy effect: When an option is dominated by another option (say if a were a subset of b), it is not choses, however this changes when the decoy is removed. The decoy effect occurs when the introduction of a subpar option causes individuals to change their preferences.
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Topic 1.2 - How would a utility graph change with the use of a decoy? What condition must the decoy fulfil?
See Brainscape Assistant 7.
| The decoy must be asymmetrically dominated by the target, meaning dominated by the target but not by the competitor.
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Topic 1.2 - Aside from the decoy effect, what is another form of menu dependence?
Compromise Effect: People tend to choose an alternative that represents a compromise. Sometimes described as resulting from extremeness aversion: a tendency to avoid options at the extreme.
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Topic 1.2 - How would the compromise effect be applied to a business framework?
A high-end brand might drive business to their expensive products by introducing a super-expensive product; though the super-expensive product might never sell.
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Topic 1.2 - WTP and WTA?
Willingness to pay
| Willingness to accept
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Topic 1.2 - The Mug Example?
3 groups created: Buyers, Sellers, Choosers.
Buyers say how much they would be willing to pay for a mug, sellers say how much they would be willing to sell a mug for, chooses say at which point hey would take money over the mug.
Outcome: Sellers and choosers are in identically the same situation, but the choosers behave more like buyers, in selecting the price they would accept money over a mug. This suggests that a low volume of trade is a result of owners' reluctance to part with their endowment.
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Topic 1.2 - Endowment Effect?
Coined by Thaler in 1980 to describe the reluctance of people to part from assets that belong to their endowment. This is present when Pb (buying price) is significantly less than Ps (selling price).
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Topic 1.2 - How could we describe the behaviour of the endowment effect?
In terms of loss aversion (a dislike of losses to a greater degree than a gain of the same size). People with an item view this item as a reference level and consider not having it to be a loss. The reference point is shifted to be inclusive of the asset for sellers, and exclusive of the asset for buyers.
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Topic 1.2 - What does a value function represent?
How an agent evaluates a change from their endowment/ reference point.
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Topic 1.2 - General form of a value function steps.
See Brainscape Assistant 8
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Topic 1.2 - Diminishing Sensitivity?
Utility/ value derived from changes further away from the reference point are smaller than outcomes close to the reference point. so 0 to 10 is better than 1000 to 1010.
The value function will be conned over losses and concave over gains.
91
Topic 1.2 - Status Quo Bias?
E.g. the mug vs chocolate allocation.
Individuals prefer the status quo to changes that involve losses in some dimensions, even when these losses are couple with gains in other dimensions. This links back to loss aversion and the money mug dilemma.
92
Topic 1.2 - What are two possible reasons for the status quo bias?
Cognitive Misperception: Perceived losses are more relevant than perceived gains and switching from the SQ may generate a loss.
Psychological Commitment: Sunk costs are relevant to justify previous commitments or investment, avoid regret or feel in control.
93
Topic 2 - What is a heuristic?
A rule of thumb or mental shortcut that requires less effort to form a judgement. They can often lead to bias and be manipulated.
94
Topic 2 - What are the three heuristic?
1. Representativeness
2. Availability
3. Anchoring and Adjustment
Note that these heuristics are not mutually exclusive and tend to overlap.
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Topic 2 - Rules of Probability:
| Pr(A u B)?
The addition rule
| Pr(A) + Pr(B) - Pr(A n B)
96
Rules of Probability: Pr(A n B)
```
Pr(A) * Pr (B|A).
Using Pr(a) * Pr(b) would overestimate the probability and would only be for independent events.
```
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Topic 2 - Bayers Rule forumla?
Pr(A|B) = [Pr(B|A)*Pr(A)]/ Pr(B)
(so Pr(BnA)/Pr(B))
The denominator expands to:
Pr(B|A) * Pr(A) + Pr(B | Not A) * Pr(Not A).
98
Topic 2 - Bayers Rule intuition?
P(Hyp/Evidence) = [P(E|H)*P(H)]/P(E)
So the probability of a hypothesis given a new piece of evidence is the probability of the evidence given the hypothesis multiplied by the probably of the hypothesis all divided by the the prior probability of the evidence.
99
Topic 2 - Base rate neglect?
When the base rate (probability of an event prior to a new hypothesis) is often left out. Leads to overestimation.
100
Topic 2 - Representativeness?
"the degree to which [an event] (i) is similar in essential characteristics to its parent population, and (ii) reflects the salient features of the process by which it is generated".[1] When people rely on representativeness to make judgments, they are likely to judge wrongly because the fact that something is more representative does not actually make it more likely.
101
Topic 2 - Law of small numbers?
In smaller samples, the chance of the probability veering from its true expected value is greater than for larger samples. Representativeness implies misconceptions of the importance of sample size and people often overgeneralise from small samples to distributions.
102
Topic 2 - Gamblers Fallacy?
Basing future events with a given probability a higher chance based on the history of events. A result of the law of small numbers.
103
Topic 2 - Anchoring and adjustment? Implications?
People begin the process of estimation with whatever information readily appears in their minds. They then reassess their initial answers based on rough notions of what is not-too-silly an answer. We tend to bias towards the anchor as our adjustments are too cautious.
104
Topic 2 - Nudges?
Based on the anchoring principle. People can be nudged towards a particular actions based on a prompt. E.g. average donation is £100.
105
Topic 2 - What can reliance on heuristics lead to.
Systematic errors.
106
Topic 2 - What are the two interacting systems of cognition according to Kahneman and Tversky?
System 1: the intuitive system uses heuristics that sometimes get things wrong from the point of view of conscious reasoning; but fast, automatic, effortless and difficult to control or modify. It is adaptive because it gets things approximately right when it is important to act quickly.
107
Topic 2 - What are the two interacting systems of cognition according to Kahneman and Tversky?
System 1: the intuitive system uses heuristics that sometimes get things wrong from the point of view of conscious reasoning; but fast, automatic, effortless and difficult to control or modify. It is adaptive because it gets things approximately right when it is important to act quickly.
System 2: Conscious reasoning. Slow and sophisticated and can be changed and improved by learning. Can only concentrate on one thing at a time and requires effort and control.
108
Topic 2 - How does choice relate to the two systems of cognition?
Choice is the product of the conical interaction between system 1 and system 2. errors or biases in judgement are the unintended side effects of generally adaptive processes.
109
Topic 2 - Conjunctive events?
Probability of two events occurring at the same time. P(AnB)
110
Topic 2 - Disjunctive events?
Probability of either one or another event occurring (disjunctive)
111
Topic 2 - Conjunction and disjunction fallacy? What is to blame?
People tend to overestimate the probability of conjunctive events and to underestimate the probability of disjunctive events.
Anchoring is to blame as the probability of success at any one stage provides a starting point for the estimation of the probabilities.
The overall probability of conjunctive (disjunctive) events is lower (higher) than the success probability at each stage, leading to overestimation (underestimation).
112
Topic 2 - Availability heuristic?
The probability of an event is often related to how easily it is brought to mind.
113
Topic 2 - Recap: What does the Representativeness Heuristic lead to?
1. Conjunction Fallacy
2. Base Rate Neglect
3. Misconceptions of importance of sample size (law of small numbers).
4. Gambler's Fallacy
114
Topic 2 - Recap: What does availability lead to?
Over and underestimation of probabilities and the conjunction/ disjunction fallacy.
115
Topic 2 - Hot Hand Fallacy?
A belief among basketball fans that a player's chance of hitting a shot is greater following a hit than following a miss on the previous shot.
The implications are similar to the gambler's fallacy in which the two independent events are considered dependent.
116
Topic 2 - Name the main example for Anchoring and and explain it.
The 'how happy are you' question.
Two questions are asked to individuals and that correlation between them is found based on the answers. The questions are asked in reverse order.
Correlation is high when the question 'how often are you dating' is asked before 'how happy are you?'.
Correlation increased from 0.11 to 0.62.
The dating question acted as an anchor.
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Topic 2 - What are the x heuristics? **
**
118
Topic 2 - Extra Space for Further addition.
.
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Topic 2 - Extra Space for Further addition.
.
120
Topic 2 - Extra Space for Further addition.
.
121
Topic 4 - Need to complete.
START AND COMPLETE.
122
Topic 4 - Intertemporal choices relates to:
the decisions involving trade-offs between costs and benefits occurring in different time periods.
123
Topic 4 - What does DUM stand for and who was it developed by?
The Discounted Utility Model which was developed by Samuelson in 1937.
124
Topic 4 - What was the DUM accepted for?
A valid normative standard for public policies (such as cost benefit analysis) and as a descriptively accurate representation of actual behaviour in analysing inter temporal choices.
125
Topic 4 - What is the basic premise of the DUM?
That people prefer money sooner than later.
126
Topic 4 - DUM: How do we denote utility streams and describe the utility at time 0 and t.
u = < u0, u1, u2, ... ut >
Where ut is the utility at time t.
uo is the utility at time 0, so today.
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Topic 4 - DUM: How would you represent the utility of stream 'u' for the point of view of t = 0? Define the delta symbol.
U^0(u) = u0 + 𝛿u1 + 𝛿^2u2 + ... + 𝛿^t ut.
= Σ𝛿^t ut for all t ≥ 0.
where 𝛿 is the discount factor and 0 < 𝛿 < 1
128
Topic 4 - DUM: 𝛿?
𝛿 is the discount factor and 0 < 𝛿 < 1
𝛿 = (1 / 1 + ρ),
ρ is the individuals pure rate of time preference or discount rate.
129
Topic 4 - What is another name for the DUM model?
The exponential discounting model.
130
Topic 4 - DUM: What are the implication if 𝛿 is:
a) Close to one;
b) Close to 0.
If 𝛿 is
a) close to 1, the person exhibits patience, as she doesn't discount their further very much.
b) close to 0, the person exhibits impatience, so discounts their future very heavily.
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Topic 4 - DUM: how would one establish an individuals discount factor, 𝛿 ? An example has been provided.
We set an amount that could be received today and ask an individual what amount would make them indifferent between the amount now and a time in the future.
```
Suppose at t = 0, you are indifferent between utility streams:
a = <2> b = <0, 6>.
U^0(a) = U^0(b), so
2 = 0 + 6𝛿
𝛿 = 1/3
```
This assumes that b is at b is the utility at t = 0 and b is the utility at t = 1.
132
Topic 4 - What is the more sophisticated version of the DUM called?
The General DUM.
133
Topic 4 - General DUM: what is the consumption profile notation?
Consumption profile: c(t), c(t+1), ..., C(T)
134
Topic 4 - General DUM: Define notationally an individuals inter-temporal utility function from the perspective of t.
U^t(c(t),...,c(T)) = ΣD(k) u(c(t+k))
From k=0 (bottom of the sigma) to T - t (top of the sigma).
c(t+k) means c subscript t + k.
135
Topic 4 - General DUM: Deine D(k) notationally and how it is interpreted?
D(k) = 𝛿^k = ( 1 / (1 + ρ) )^k
It is interpreted as the person's discount function: the relative weight that she attached, in period t, to her well-being in period t + k.
136
Topic 4 - General DUM: how is u(c(t+k)) often interpreted?
As the person's cardinal instantaneous utility function: her well-being in period t + k.
137
Topic 4 - General DUM: What does ρ represent?
An individuals pure rate of time preference AKA discount rate.
It reflects the collective effects of the psychological motives.
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Topic 4 - General DUM: How could we represent notationally the discount factor and discount rate in terms of each other?
```
Discount Rate = ρ = (1 - 𝛿) / 𝛿
Roe is Rate (the percentage in decimal form.
Discount Factor = 𝛿 = 1 / (1 + ρ)
Delta is factor.
0 < 𝛿 < 1
```
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Topic 4 - DUM: What are some potential implications in life if your discount factor is low that would not necessarily be irrational?
1. Spend more money;
2. Procrastinate;
3. Do drugs
Gratification is preferred in the shorter time horizon.
140
Topic 4 - DUM: What is Gary Becker's theory of rational addiction?
That, given a very low discount factor, heavy drug abuse, for example, can be perfectly rational.
141
Topic 4 - What is the main requirement of DUM?
That one discount factor/ rate is consistently applied.
142
Topic 4 - Foundations of DUM: What are the 6 Assumptions?
1. Integration of new alternatives with existing plans.
2. Consumption Independence.
3. Stationary Instantaneous Utility.
4. Independence of discounting from consumption.
5. Constant Discounting
6. Diminishing Marginal Utility and Positive Time Preferences.
143
Topic 4 - Foundations of DUM: 1. Integration of new alternatives with existing plans explanation?
A person exaltations evaluates new alternatives by integrating them wit hone's existing plans.
144
Topic 4 - Foundations of DUM: 2. Consumption Independence explanation?
A persons well-being in period t + k is independent of her consumption in any other period.
145
Topic 4 - Foundations of DUM: 3. Stationary Instantaneous Utility explanation?
The cardinal instantaneous utility function u(ct) is constant over time.
Where ct has a subscript case t.
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Topic 4 - Foundations of DUM: 4. Independence of discounting from consumption explanation?
All forms of consumption, costs and benefits, are discounted at the same rate.
This is central to the notion of unitary time preference and enabling us to discount between objects, not just between the object being delayed
147
Topic 4 - Foundations of DUM: Constant Discounting explanation? What does it imply?
Implies time-consistency.
At any period of time people use the same discount rate for all future periods.
Delaying two dated outcomes by a common amount should not change preferences between the outcomes.
148
Topic 4 - Foundations of DUM: 6. Diminishing Marginal Utility and Positive Time Preferences explanation?
Diminishing marginal utility: The instantaneous utility función u(ct) is concave.
Leads to consumption being spread over time.
Positive time preference: discount rate ρ is positive. Motivates people to concentrate consumption in the present.
149
Topic 4 - What are the violations of DU seen empirically?
1. ρ (discount rates) are not constant, but decline over time.
2. Discount rates vary across different types of inter-temporal choices: gains are discounted more than losses, small amounts more Thant large amounts, sequences of multiple outcomes are discounted differently than outcomes considered singly.
150
Topic 4 - DUM: Evidence against a constant ρ and its name? How did Thaler show this?
Short Term Impatience:
Thaler showered that the discount rate over longer horizons is lower than the discount rate over shorter time horizons.
Subjects asked how much they would be required to received in 1 month, 1 year and 10 years to forfeit $10 today. The annualised results shoes that the annual discount rate fell as time increased.
This is known as HYPERBOLIC DISCOUNTING.
151
Topic 4 - Evidence against DUM: Hyperbolic Discounting modelling?
See Brainscape Assistant 9.
| We replace the discount factor D(k) with a new term, basically swapping ρ to ρ
152
```
Topic 4 - The Discount Rate:
1. Postpone Receipt
2. Postpone Payment
3. Expedite Receipt
4. Expedite Payment implications?
Short Term Impatience?
```
Short Term Impatience - The discount factor is greater (rate lower) the longer one has to wait.
153
```
Topic 4 - The Discount Rate:
1. Postpone Receipt
2. Postpone Payment
3. Expedite Receipt
4. Expedite Payment implications?
Absolute Magnitude Effect?
```
Absolute Magnitude Effect - The larger the sum of money, the larger the estimated discount factor, suggesting people are more patient for larger amounts.
154
```
Topic 4 - The Discount Rate:
1. Postpone Receipt
2. Postpone Payment
3. Expedite Receipt
4. Expedite Payment implications?
Gain Loss Asymmetry?
```
Gain Loss Asymmetry - The estimated discount factor is smaller for gains than losses (so people would prefer to receive money more quickly and pay it more slowly)
155
```
Topic 4 - The Discount Rate:
1. Postpone Receipt
2. Postpone Payment
3. Expedite Receipt
4. Expedite Payment implications?
Delay-speed-up asymmetry?
```
Delay-speed-up asymmetry - The estimated discount factor is higher to postpone than to expedite payment, and higher to expedite than postpone receipt. (one prefers to receive sooner and pay later).
156
Topic 4 - What is the intuitive understanding of the discount rate (time to receive/ pay money)?
The higher the discount rate, the more time one is willing to wait before paying or receiving money (the lower the discount factor, roe). The higher the factor, the lower the payment one would have to receive in order to delay receipt or payment.
157
```
Topic 4 - The Discount Rate:
1. Postpone Receipt
2. Postpone Payment
3. Expedite Receipt
4. Expedite Payment implications?
OVERALL IMPLICATIONS?
```
The discount factor changes depending on context, contradicting the DUM, which states that the discount factor is independent of consumption type and constant over time.
The appropriate discount factor should therefore be thought about for each particular situation.
158
Topic 4 - The Utility of Sequences Implications? Set out scenario as well (visiting and aunt you don't like and visiting friends on two visits to a place)? Lowenstein and Prelec (1993).
Hint: Relate to exponential discounting.
When the two reps are close together, most people opted to visit the aunt first. When the two trips were further apart, most people decided to visit the friend first.
Implications: This shows a PREFERENCE FOR AN IMPROVING SEQUENCE, which goes against what exponential discounting would predict. With a discount factor < 1, ED would predict that the individual would visit the friend first because they are impatient for higher utility.
Impatience becomes apparent as the gap becomes bigger though and the results revert back to those expected by EDM.
159
Topic 4 - What can the Quasi Hyperbolic Discounting model be used to explain? What is another name for this model?
Reversals in time utility preference.
Preferences between two delayed rewards can reverse in favour of the more proximate reward as the time to both rewards diminishes. Q-Hyperbolic discounting can explain preference reversal if the β value is sufficiently low.
AKA the Beta-delta function.
160
Topic 4 - Define notionally the Quasi-Hyperbolic Discounting Function.
Brainscape Assistant 10.
161
Topic 4 - Quasi-Hyperbolic Discounting Function: β meaning and understanding if
a) β = 1
b) β < 1
β is the present bias.
a) If β = 1, an individual who discounts the future quasi-hyperbolically will behave the same as an individual who discounts the future exponentially.
b) If β < 1, all outcomes beyond the present time are discounted more than under exponential discounting.
162
Topic 5 - Homoeconomus?
Assumed to be both rational and self-interested.
163
Topic 5 - How would we say that the utility of one person depends on the utility of another (e.g. giving to charity)?
There are Social or Other-regarding preferences.
164
Topic 5 - What games present evidence for social preferences? (3)
1. Dictator game
2. Ultimatum game
3. Linear good game.
165
Topic 5 - What alternative model is used to represent inequality aversion?
The Fehr-Schmidt Model of Inequality aversion.
166
Topic 5 - The Dictator Game - Explain the game.
Players
Scenario
Final
1. The dictator game involves two people, the PROPOSER and RECEIVER.
2. The proposer receives £10 and is asked how much he would like to give to the receiver.
3. The game ends (one shot game)
167
Topic 5 - The Dictator Game - What is the outcome and how does this compare with the standard model?
How does the result change when we have a single-blind treatment and double blind treatment?
We would expect under a self interested individual to take all the money. We find that the majority give more than 0.
In the single-blind treatment (researcher sees amount), we can argue that the participant may wish to appear as nice to the researcher, so gives some money.
In the double blind treatment, the researchers also do not know the amount given.
People give a similar amount in the double blind.
168
Topic 5 - The Ultimatum Game - Explain the game.
Participants
Scenario
When the game is accepted
1. The Ultimatum Game involves two people, a Proposer and Receiver.
2. The proposer is given an amount and is asked how much of this he wants ogive to a receiver. The proposer makes a take-it-or-leave-it offer.
3. If the responder accepts the offer, they both receive the specified amounts. If the responder rejects, they both get nothing.
169
Topic 5 - The Ultimatum Game - What do we empirically observe?
What we expect and the outcome.
We would expect the receiver to accept any amount as it increases their income. We see that a large number of offers are rejected that are below the 50% split. (40% rejects when the plot is 60/40)
170
Topic 5 - The Ultimatum Game - - Results?
Typical Results
What are the results robust to
When does it vary.
Typical Results
No offers above .5 and at the average offer around .4. Few offers below 0.2
What are the results robust to?
Higher stakes and experience
When does it vary?
Age and Culture.
171
Topic 5 - Linear Public Good Game - Explain the Game.
Participents
Scenario
Pareto Efficient
Nash Equilibrium
We ave 4 people who are each given some money. They are asked how much they wish to donate to a group project.
Any money contributed is increased 1.6x, and then split..
Pareto efficient outcome: everyone to contribute.
A person interested only in their own materials payoff would not contribute to the group project, and the Nash Equilibrium is for no-one to donate anything.
172
Topic 5 - The Ultimatum Game - Results?
Typical Results
What are the results robust to
When does it vary.
Typical Results
No offers above .5 and at the average offer around .4. Few offers below 0.2
What are the results robust to?
Higher stakes and experience
When does it vary?
Age and Culture.
173
Topic 5 - Linear Public Good Game - Explain the Game.
```
Participants
Scenario
Rounds
Pareto Efficient
Nash Equilibrium
```
We have 4 people who are each given some money. They are asked how much they wish to donate to a group project.
Any money contributed is increased 1.6x, and then split..
Pareto efficient outcome: everyone to contribute.
The game is played multiple times.
A person interested only in their own materials payoff would not contribute to the group project, and the Nash Equilibrium is for no-one to donate anything.
174
Topic 5 - Linear Public Good Game - Observations
Punishment vs no punishment
Common Participants vs no partner.
Conclusion.
Partner Games (the same people for 10 rounds) and punishment both lead to people donating more money as the game goes on.
Stranger (4 randomly matched people) games and no punishment lead to less money being donated as the game goes on.
Giving and taking is conditional on others' behaviour: reciprocity.
175
Topic 5 - Linear Public Good Game WITH PUNISHMENT - Explain the game.
Each person can pay an amount to punish another player in the second stage.
176
Topic 5 - Can we have transitive and complete preferences for people donating to charity etc?
Yes, if they derive more utility/ satisfaction from being kind to having money.
177
Topic 5 - Preferences - Inequity Aversion?
A preference for equal payoffs.
178
Topic 5 - Preferences -Reciprocity?
A preference from repaying kindest with kindness and meanness with meanness.
179
Topic 5 - Preferences - Altruism?
Caring for others' payoff or utility.
180
Topic 5 - Preferences - Preferences for social approval?
A preference to be liked by others.
181
Topic 5 - What are the 4 non-standard preferences?
Inequality Aversion
Reciprocity
Altruism
Preferences for Social Approval.
182
Topic 5 - How would we model inequality aversion - overview?
The Fehr-Schmidt Model of Inequality aversion.
An inequality averse person get disutility from earning more or less than other people.
So, aswell as assuming that some people are self interested, we also assume some people are motivated by fairness.
183
****Topic 5 - Lay out the Fehr-Schmidt Model of inequality aversion. What are the symbols used and their implications.
**** Brainscape Note ***
β: Advantageous Inequality - Associated with the disutility received when receiving more than others.
αi: Disadvantageous Inequality - Associated with the disutility received when receiving less than others. This is always higher than β as people are more averse to others having more than having more themselves.
β < αi
0 ≤ β < 1
αi has no upper limit.
x = (xi, xj) - Payoff of Individuals
184
****Topic 5 - Lay out the Fehr-Schmidt Model of inequality aversion. What are the symbols used and their implications.
```
**** Brainscape Note ***
β: Advantageous Inequality - Associated with the disutility received when receiving more than others.
αi: Disadvantageous Inequality - Associated with the disutility received when receiving less than others. This is always higher than β as people are more averse to others having more than having more themselves.
β < αi
0 ≤ β < 1
αi has no upper limit.
x = (xi, xj) - Payoff of Individuals
Agent does not like to be better
```
185
Topic 5 - Ultimatum Game with inequality averse preferences (analysed with the Fehr Schmidt Model of Inequality Aversion with one player who is inequality aversion) - Notation?
```
A offers a share of s to B.
If B accepts, A received 1 - s of X.
So
Reject: (xA, xB) = (0,0)
Accept: (xA, xB) = ((1-sX, sX)
```
186
Topic 5 - Ultimatum Game with inequality averse preferences (analysed with the Fehr Schmidt Model of Inequality Aversion with one player who is inequality aversion) - Expected Responses?
B will accept if offer is 0.5
| B will accept if offer > 0.5
187
Topic 5 - NOTE ON 21/34
**
188
Topic 5 - When would a Inequality Averse Responder reject an offer under the Fehr Schmidt Model of Inequality Aversion in the Ultimatum Game?
s < *******
