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Behavioral Economics And Psychology > Final Exam > Flashcards

Final Exam Flashcards

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1
Q

Cumulative Prospect Theory (CPT)

A

Issue with original PT is it allowed for the selection of dominated lotteries.

CPT fixes this by imposing ∑𝜋(𝑝_𝑖)=1

Economists usually cite CPT while Psychologists cite PT

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2
Q

Nash Equilibrium

A

Definition: A set of strategies in a game where no player can benefit by changing their strategy while the other players keep theirs unchanged.

Example: In the Prisoner’s Dilemma, both prisoners choosing to squeal is a Nash Equilibrium because neither can unilaterally reduce their prison time by changing their strategy.

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3
Q

Allais Paradox

A

Participants’ choices contradict the independence axiom. They usually prefer a certain gain over a probabilistic gain of higher expected value in gambles 1 and 2, but reverse preference by choosing gamble 4 when comparing 3 and 4.

Gamble 1: (1 million, 1)
Gamble 2: (1 million, .89; 5 million, 0.1; 0, .01)

Gamble 3: (1 million, 0.11; 0, .89)
Gamble 4: (5 million, .1; .9, 0)

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4
Q

WARP (Weak Axiom of Revealed Preferences)

A

Definition: If option A is chosen over B when both are available, then A should always be chosen over B, regardless of other options.

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5
Q

Certainty Equivalent

A

Definition: The guaranteed amount of money that someone would accept instead of taking a gamble with a higher, uncertain payout.

Example: Accepting a guaranteed $40 instead of a 50% chance at $100.

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6
Q

DU and Time Consistency

A
  • Intertemporal Choice is Time Consistent if the preference between choices remains consistent through time.
  • Time Consistency is a requirement of DU.
  • Violating Time Consistency means you can’t be a DU Maximizer!

Examples:
1. For the $100 Sooner or Later scenario, you first state that you prefer foregoing an extra $1 in one week in favor of $100 now, but that 50 weeks from now, you instead prefer waiting one week for the extra $1

  1. For the Broken Resolutions scenario, you plan to be healthy, but when the time comes to execute your plan, you succumb to temptation and eat the Cookie
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7
Q

Game Theory Assumptions

A
  1. All players are maximizing their payoffs/utilities
  2. All players have common knowledge about the rules of the game
  3. Each player’s payoff depends on actions taken by all players
  4. Each player has Complete Information unless otherwise specified: payoffs are common knowledge among all players
  5. Each player has Perfect Information unless otherwise specified: player knows full history of the game (i.e. previous Chess moves)
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8
Q

Prisoner’s Dilemma

A

Concept: A fundamental game in game theory illustrating that two individuals might not cooperate, even if it appears that it is in their best interests to do so.

Example: Two criminals are arrested and must decide independently whether to confess. Confessing (squealing) might benefit them individually but not collectively.

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9
Q

Pareto Optimality

A

Definition: A state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.

Example: In a different context, allocating hours of operation between two departments in a way that maximizes overall productivity without overburdening any single department.

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10
Q

Game Theory

A

Definition: A branch of mathematics that studies strategic interactions where the outcomes depend on the actions of multiple agents, each trying to maximize their own payoff.

Example: Strategic decisions in business, such as pricing products or choosing production levels, where outcomes depend on competitors’ actions.

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11
Q

IA Weaknesses

A

Inequity Averse Utility does better than Selfish Utility in predicting behavior in social choice games

However, as IA Utility is formulated solely by outcomes, it would not be able to capture certain factors like:

  1. Anonymity of participants
  2. Source of funds (earned, gift, etc.)
  3. Nature of recipient (charity, friend, etc.)
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12
Q

Expected Value

A

Definition: The sum of all possible values each multiplied by the probability of its occurrence.

Example: A lottery ticket offering a 50% chance of $100 and 50% of $0 has an EV of $50.

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13
Q

Market Monopsony Game

A

Each individual in the class chooses how to split $100 with the Professor, but only the best offer accepted.

Selfish NE to offer $100. Best case scenario is you make $1 by offering $99.

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14
Q

Evaluating BDU

A

Pros
1. Future gets discounted to the Present
2. Time further into the future gets discounted more
3. Accommodates time inconsistent behavior

Cons
1. Requires an additional 𝛽 discount term (more complex than DU)

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15
Q

Common Ratio Effect

A

Concept: A violation of the expected utility theory where changing the probabilities of outcomes proportionally across gambles affects preferences.

For higher probabilities of gain, most prefer the larger probability, smaller gain option.

But when the probabilities of gain are low, most prefer the riskier option with the higher gain.

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16
Q

Completeness and Transitivity

A

Completeness: Every pair of alternatives can be compared.

Transitivity: If option A is preferred to B, and B is preferred to C, then A should be preferred to C.

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17
Q

Sign Effect

A

The steeper discounting of gains compared to losses.

Thaler suggests this is related to Loss Aversion: losses are out of pocket, so not willing to pay much more for a delay

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18
Q

Inequity Aversion in the Ultimatum Game

A

Proposer will offer a percentage “s” of their allocation

  1. Proposer who very strongly dislikes having more than Receiver (𝛽_1>0.5) will offer exactly 50%
  2. Proposer with 𝛽_1<0.5 will offer the minimum acceptable offer

Predictions are consistent with observed behavior of no offers above 50%, many within 40%-50%, and few low offers.

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19
Q

Sequences Effect

A

As it relates to wages, workers prefer an increase year over year vs. a flat structure or decreasing structure even if the wages are exactly the same over a period.

Sequences should not impact preference over time in DU and BDU, just discount each amount and add them up and choose the highest!

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20
Q

Splitting $10 Example

A

Concept: How individuals decide to split a sum of money in social settings, influenced by factors such as fairness, anonymity, reputation, and potential retribution.

Example: Deciding whether to split $10 equally with a professor or take a larger share for oneself based on various personal and social considerations.

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21
Q

Dictator Game

A

Game consists of a Dictator and one or more other Recipients

The Dictator is the only player who can act

The Dictator decides how they want to split an amount of money with the Recipient

Selfish NE is for the Dictator to offer nothing

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22
Q

Level-k Reasoning & Keynes Beauty Contest

A

The idea is people are of different levels of strategic reasoning:

Level-0 player guesses randomly, 50∗0.5^0=50 on average

Level-1 player guesses 50∗0.5^1=25

Level-2 player guesses 50∗0.5^2=12.5

Level-∞ player guesses 50∗〖0.5〗^∞=0, which is NE

Every level player thinks there are no levels above them.

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23
Q

Beta-Delta Utility (BDU)

A

The Beta-Delta Utility (BDU) of an item/money 𝑥 received T periods into the future is

BDU(𝑥, T)=

{ 𝑢(𝑥), T=0
{ 𝛽𝛿^T∗𝑢(𝑥), T>0

where 𝛽<1, 𝛿<1

Decision Rule: Choose the option that maximizes BDU

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24
Q

Compound Interest Formula

A

FV=PV∗(1+𝑟)^T

t in months or years
r = interest rate

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25
Q

Normative vs. Positive Theories

A

Normative Theories: Prescriptive, suggesting how decisions should be made.

Positive Theories: Descriptive, explaining how decisions are actually made in practice.

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26
Q

Risky Choice

A

Definition: Making a decision where outcomes are uncertain but associated probabilities are known.

Example: Tossing a coin where heads might win you $10 and tails wins nothing.

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27
Q

NE vs Level-k

A

NE is viewed as the purely rational solution concept

Level-k may do better in predicting actual behavior when:
1. NE are difficult to compute or reason
2. Players HAVE varied understanding of game or optimal behavior
3. Players ASSUME varied understanding of game or optimal behavior

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28
Q

NE and DE

A
  • Every Dominant Equilibrium (DE) is a Nash Equilibrium (NE)
  • Not Every NE is a DE
  • Every finite game has a NE
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29
Q

Risk Preferences

A

Risk Averse: Preference for certain outcomes over gambles with the same expected outcome.

Risk Neutral: Indifference between certain outcomes and equivalent gambles.

Risk Loving: Preference for gambles over certain outcomes with the same expected outcome.

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30
Q

Nash Equilibrium in the Coordination Game

A

Game: You and professor each pick heads or tails. Values assigned to each of the four possible combos.

Example 1:
(H,H) and (T,T) = 1
(H,T) and (T,H) = 0
Result: NE is either of the options that equal 1, but the outcome could be anything due to the inability to coordinate.

Example 2:
(H,H) = (2,2)
(T,T) = (1,1)
(H,T) and (T,H) = (0,0)
Result: NE is h,h or t,t but outcome will be h,h.

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31
Q

Ultimatum vs. Monopsony

A

The Ultimatum Game results starkly varied from the Selfish NE

The Monopsony Game results were close to the Selfish NE

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32
Q

Exponential Discount Factor

A

PV=FV∗(1/((1+𝑟) ))^T

PV=FV∗𝛿^T

𝛿 (Delta) is the Exponential Discount Factor

Discount Factor = 1/((1+ interest Rate))

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33
Q

Delayed Gratification

A

The most famous and influential time discounting study is likely the Mischel Marshmallow Experiment. Preschoolers could eat one marshmallow or wait 15 minutes for three marshmallows.

Delayed gratification was a strong predictor of:

  1. High future self-control and successful pursual of goals
  2. High parental ratings of attention and intelligence
  3. Higher SAT scores
  4. Improved mental health and self-esteem
  5. Reduced drug consumption
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34
Q

Social Choice

A

Definition: Social choice theory studies decision-making processes that affect multiple individuals, focusing on how collective decisions are made based on individual preferences.

Example: Choosing how to allocate a budget within a community project, balancing the different needs and preferences of community members.

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35
Q

Three Approaches to Choice

A

Utility-Only Approach: Decisions are made solely based on utility maximization.

Preference Approach: Choices are based on personal preferences, which could be ranked or unranked.

Revealed Preference Approach: Choices are inferred based on observed behaviors.

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36
Q

Modifications of Theoretical Models

A

Concept: Adjusting theoretical models based on empirical data to better reflect observed behaviors.

Example: Modifying preference axioms when real-world data show consistent violations.

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37
Q

Risky Lotteries Evaluation

A

Concept: Analyzing different lotteries based on their expected utility rather than just expected value.

Example: Choosing between a lottery with a high probability of a modest win and a low probability of a large win.

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38
Q

Hormones and the Ultimatum Game

A

Testosterone reduces generosity and oxytocin increases generosity

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39
Q

Experimental Tests of Theories

A

Concept: Validating theoretical models by comparing predictions with actual decision-making behavior in controlled experiments.

Example: Using a lab setting to test if people’s choices align with predicted utility maximization.

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40
Q

Certain Choice

A

Definition: Decision-making process where each option is received with 100% certainty.

Example: Choosing an apple over an orange with no chance of outcome variation.

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41
Q

St. Petersburg Paradox

A

A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The initial stake begins at 2 dollars and is doubled every time tails appears. The first time heads appears, the game ends and the player wins whatever is the current stake. What would be a fair price to pay the casino for entering the game?

Expected value = infinity, highlighting limitations of using expected value to make real-life choices.

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42
Q

Independence of Irrelevant Alternatives (IIA) Violation

A

Concept: Preference between two options should not depend on the presence of a third option.

Example: Choice between gambles is influenced by the introduction or removal of another unrelated gamble.

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43
Q

Discounted Utility (DU)

A

The Discounted Utility (DU) of an item/money 𝑥 received T periods into the future is

DU(𝑥, T)=𝛿^T∗𝑢(𝑥); where delta < 1

Decision Rule: Choose the option that maximizes DU

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44
Q

Intertemporal Choice

A

Definition: Choices involving trade-offs among costs and benefits occurring at different times.

Example: Deciding whether to receive $100 now or $110 one year from now.

45
Q

Preference Reversals

A

Definition: A situation in which the preference between options changes depending on how they are evaluated (e.g., choice vs. pricing tasks).

Example: Preferring a low-risk option in direct choice but assigning a higher monetary value to a high-risk option when pricing them separately.

46
Q

Ultimatum Game

A

Concept: A game in which one player, the proposer, offers how to divide a sum of money with another player, the responder, who chooses to accept or reject the proposal. If the responder rejects the offer, both players get nothing.

Example: Offering $5 out of $10 to another player, who must accept for both to receive the money, or reject, resulting in no one receiving anything.

47
Q

Keynes Beauty Contest

A

Game: Choose a number from 0 – 100. Whoever chooses half the average wins.

NE = everyone choose 0, but no one does this

Game uses level-k reasoning

48
Q

Regret Theory

A

Definition: Suggests that people anticipate regret from their decisions and choose in a way to minimize this expected regret.

Example: Avoiding a high-risk investment to prevent potential regret of large losses.

49
Q

Examples of Intertemporal Choice

A
  1. Saving for Retirement
  2. Education Investment
  3. Health Choices with long-term benefits but require immediate effort and sacrifice
  4. Saving for larger purchases or investments in the future
  5. Environmental Conservation
50
Q

Discounting Anomalies

A
  1. Magnitude Effect
  2. Sign Effect
  3. Delay-Speedup Asymmetry
  4. Hidden Zero
  5. Sequences
  6. Independence/IIA
51
Q

Discounted Value Limitations

A
  1. What if dollars are not valued equally?
  2. What about if the items of choice are NOT money?
52
Q

Loss Aversion

A

Definition: The tendency to prefer avoiding losses to acquiring equivalent gains.

Example: Being more upset by losing $50 than being pleased by gaining $50.

53
Q

Social Choice

A

Definition: Decisions that involve multiple individuals’ preferences or social welfare.

Example: Voting on a policy that affects tax distribution.

54
Q

Framing Effect

A

Concept: Decisions are influenced by the way choices are posed or framed.

Example: Responding differently to a choice depending on whether it is presented as a loss or a gain.

55
Q

Dominant Strategy

A

Definition: A strategy that results in the highest payoff for a player, no matter what the other players do.

Example: In the Prisoner’s Dilemma, squealing is a dominant strategy because it always leads to a better or equal payoff compared to staying silent, regardless of the other player’s choice.

56
Q

Evaluating DU

A

Pros
1. Time further into the future gets discounted more
2. Normative: it is an easy, natural extension of Expected Utility
3. Links up nicely with Compound Interest Formula

Cons
1. Cannot accommodate time inconsistent behavior
a. Each time interval is equally
weighted ($100 Sooner or
Later)
b. Doesn’t allow for temptation,
procrastination (Breaking
Resolutions)

57
Q

Ambiguous Choice

A

Definition: Decisions made under conditions where the probabilities of outcomes are not known.

Example: Investing in a new startup without clear historical performance data.

58
Q

Keys to Willpower

A
  1. Redirect attention
  2. Framing: focus on cooler representations of the temptation. Think of a marshmallow as a cloud instead of food.
  3. Avoid temptation: remove yourself from situations in which you are exposed to temptation, as willpower consumes costly energy.
  4. Give in to minor temptations: if you need to study and not procrastinate, research shows that giving into more harmless temptations (eating chocolate) can reduce procrastination, as maintaining willpower is costly!
59
Q

Marginal Utility

A

Definition: The additional satisfaction or utility gained from consuming one more unit of a good or service.

Example: The utility gain from consuming a third slice of pizza compared to the second.

60
Q

Expected Utility Theory

A

Concept: Decision-making model that accounts for risk aversion by using utility values rather than expected payouts.

Example: Preferring a certain payoff of $50 over a 50% chance of $100, despite the same expected value.

61
Q

Now not later: $100 example

A

Why would you prefer $100 today over $100 a year from now?

  1. Death: Chance you won’t live until next year
  2. Future: You are not the “one year from now” You
  3. Interest: Put the $100 in the bank and get $100 plus Interest
  4. Inflation: $100 now can buy more than $100 next year
62
Q

Inequity Aversion

A

Definition: A preference for fairness and a resistance to inequitable outcomes, even at a cost to oneself.

Example: A person might prefer to receive less money than to see a disproportionate split in an economic game, even if it means receiving less overall.

63
Q

Utility Function

A

Definition: A mathematical representation that assigns a numerical value to each possible choice to reflect its overall utility to the individual.

Example: U(Apple) = 2; U(Orange) = 1; apples are twice as preferred as oranges.

64
Q

Delay-Speedup Asymmetry

A

The delay/speed-up asymmetry implies higher discount rates for decisions involving delayed rewards than for decisions involving immediate rewards

65
Q

Coordination Game

A

Concept: A game where the payoff to each player depends on the actions of both and where multiple Nash Equilibria can exist, often requiring players to coordinate their choices.

Example: Two drivers at an intersection must choose whether to go or stop. Both choosing to go or stop can be equilibrium outcomes, but coordination is required to avoid accidents.

66
Q

Inequity Aversion (IA) in the Monopsony Game

A

Since IA players prefer to be better off instead of worse off than others (𝛼_𝑖≥𝛽_𝑖), there is an incentive to win

IA players will have the incentive to continually undercut prospective proposals of others to win

This pushes the IA NE proposal equal to the Selfish NE: offer everything!

67
Q

Finding Nash Equilibrium

A

To identify if a strategy/action set is a Nash Equilibrium, it must be a mutual best response, so no player has an incentive to unilaterally deviate

Unilateral deviation means one player switches action/strategy while holding all other players’ actions/strategies fixed

68
Q

Prospect Theory

A

Prospect Theory (PT) uses probabilities 𝑝_𝑖 evaluated by a probability weighting function 𝜋(𝑝), and outcomes 𝑥 evaluated by a value function 𝑣(𝑥):

PT(𝐿)= SUM (𝜋(p) * v(x))

Key Concept: Loss aversion - losses are felt more intensely than equivalent gains.

69
Q

Trust Game

A
  • Game consists of a Sender and a Receiver
  • Sender can send any of their money to the Receiver
  • The Receiver receives x times the money sent (often 3 times)
  • The Receiver can then send any amount back to the Sender
  • The Sender exhibits Trust by sending money
  • The Receiver exhibits Trustworthiness by returning money

Selfish NE is for the Sender to send nothing and Receiver to return nothing

70
Q

Dictator Demographics

A
  1. Sharing increases with age
  2. Students most consistent with Selfish NE
  3. Elderly never play NE
  4. Female Dictators give more than Male Dictators
  5. Female Recipients get more than Male Recipients
  6. Race has no effects
71
Q

Discounted Value

A

Similar concept to Expected Value where each dollar is valued equally (Constant Marginal Utility of Wealth)

PV=FV∗𝛿^T

72
Q

Independence/IIA Affecting DU

A

Each outcome in a sequence should be independently discounted, and the option with the highest discounted sum should be chosen. However, this is not the case in the example of eating at home or at fancy restaurants on different weekends.

73
Q

Hidden Zero Effect

A

Definition: Representing a single choice as an extended sequence reduces impulsive choice.

Example:
Hidden Zero
$5 today
$7 last day of class
Explicit Zero
$5 today, $0 last day of class
$0 today, $7 last day of class

74
Q

Beta-Delta (Hyperbolic) Discounting

A

Hyperbolic Discounting means a Varying discount factor with time

Exponential Discounting means a Constant discount factor with time

75
Q

Magnitude Effect

A

Higher amounts of money are discounted LESS

High Discount Rate 𝑟 ⟺ Low Discount Factor 𝛿 ⟺ High discounting
Low Discount Rate 𝑟 ⟺ High Discount Factor 𝛿 ⟺ Low discounting

76
Q

Present Bias

A

Present Bias: The Present gets a Premium relative to all Future times

Every time increment gets discounted by the same 𝛿 under DU, but maybe there’s a bigger valuation difference between certain days.

77
Q

Rationality

A

Definition: If a preference relation satisfies Completeness and Transitivity, then it is Rational

Complete + Transitive = Rational

78
Q

Utility Representation of Preference

A

Definition: A function 𝑢( .) represents a preference relation ≽ if for all 𝑥,𝑦 ∈ 𝑋,𝑥 ≽𝑦 ⇔ 𝑢(𝑥) ≥ 𝑢(𝑦)

Rationality is a NECESSARY condition for a utility function representation of preferences.

79
Q

Ordinal Utility

A

Theorem: All positive monotonic transformations of 𝑢 represent the same preference!

Utility functions with this property are called ORDINAL

80
Q

Positive monotonic transformation

A

A monotonic transformation is a way of transforming one set of numbers into another set of numbers in a way that the order of the numbers is preserved.

The “positive” part means the transformation has a positive slope

81
Q

Criticism of Preference Approach

A

Preferences are not observable

If we are interested in Choice, make Choice the foundation

Samuelson pioneers the Revealed Preference Approach in 1930s

Are the preferences revealed from observed choice consistent with utility maximization?

82
Q

About Normative Theory

A

No data, observation or experiments are required for Normative Theory

A useful Normative Theory should be able to be tested and proven false (falsifiable)

83
Q

Econ vs Psych

A

Historically, Economic Theory of Choice was motivated more by Normative principles (choice should obey WARP, preferences should be transitive, etc.)

Psychology Theory of Choice is arguably more motivated by Positive principles (people’s observed choices obey WARP, people’s preferences are consistent with transitivity, etc.)

84
Q

Normative Features of Choice Theory

A
  1. Completeness (Preference Approach)
    -People SHOULD know how they feel about any two things
    -People SHOULD NOT be able to say they don’t know
  2. Transitivity (Preference Approach)
    - People SHOULD exhibit such consistency
    - Otherwise, they could be robbed by a money pump scheme
  3. WARP (Revealed Preference Approach)
    - If someone chooses A in a choice scenario in which B was also available, then they should never choose B when A is available in any other scenario
85
Q

Mental Accounting

A

Mental accounting interprets the tendency of people to mentally segregate their financial resources into different categories. In the event of financial losses or gains in different mental accounts, people will be impacted differently than if the financial loss was integrated across their entire financial portfolio.

Example: losing theater ticket or losing $10 poll

86
Q

Factors Impacting Stability of Preferences

A
  1. Psychological/Mental Accounts
  2. Relative Valuations
  3. Positive Attribute vs Negative Attribute Framing
  4. Separate vs Joint Evaluation
  5. Arbitrary Anchoring
  6. Endowment Effect/Ownership Rights
  7. Defaults
  8. Attraction/Decoy/Asymmetric Dominance Effect
  9. Compromise Effect
87
Q

Relative Valuation (Relativity Trap)

A

In a relativity trap, buyers may perceive a relative difference in prices as more important than an absolute difference, even though the absolute difference reflects what they actually save or pay for a good better than the relative difference.

Example: Buying a coat and calculator from the same store or different stores poll

88
Q

Attribute Framing

A

Subjects told to rate either 75% lean ground beef burger (Positive) or 25% fat ground beef burger (Negative) on a fat-lean scale

These burgers are the same fat content: 75% lean implies the other 25% is fat!

The lean-framed burgers were rated as more than 2 rating levels leaner on a 7-level rating scale

89
Q

Separate vs. Joint Evaluation

A

Completeness suggests evaluating options separately or jointly should not influence the valuation. However, the resume example (with candidates’ GPA and experience given) proved that the two candidates were judged differently based on separate or joint evaluation.

90
Q

Decoy Effect

A

Given options by Competitor and Target that have tradeoffs

Add a third Decoy option dominated by Target only

The third Decoy option attracts choices toward the Target option that dominates it and away from the Competitor

Also called Asymmetric Dominance Effect

91
Q

Compromise Effect

A
  • Two options that have tradeoffs, B and C
  • Add a third distant option A that is not dominated by B or C
  • B now looks like a compromise between the extremes A and C

𝐶(B, C)=C
𝐶(B, C, A)=B
This violates WARP!

92
Q

Condorcet Paradox (Group Intransitivity)

A

Consider 3 voters with preferences for candidates 𝑥,𝑦,𝑧:
Voter 1: 𝑥≻𝑦≻𝑧
Voter 2: 𝑦≻𝑧≻𝑥
Voter 3: 𝑧≻𝑥≻𝑦

Aggregate:
𝑥≻𝑦 (Voters 1 and 3)
𝑦≻𝑧 (Voters 1 and 2)
𝑧≻𝑥 (Voters 2 and 3)

Transitive individual preferences create intransitive cycles in aggregate!

93
Q

Groups with more intransitivity

A
  1. Elementary school kids
  2. Older adults
  3. People with mood disorders
94
Q

Cardinal Utility

A

Under EU, utility functions are no longer Ordinal, they are Cardinal

Cardinal Utility means that utility values have some meaning outside of just Ordinal ranking

Absolute magnitudes are still meaningless:
𝑢^∗ (“Apple” )=3 and 𝑢^(∗∗) (“Apple” )=6 give no information about Apple utility

Differences in utility now have meaning:
(𝑢^(∗∗∗) (“Apple” )− 𝑢^(∗∗∗) (“Orange” )) > (𝑢^(∗∗∗) (“Orange” )−𝑢^(∗∗∗) (“Pear” )) means that an Apple’s preference over Orange exceeds an Orange’s preference over Pear

95
Q

Positive Linear Transformations

A

Under EU, any Positive Linear Transformation of 𝑢 represents the same preference as 𝑢.

𝑢 is unique up to a positive linear transformation under EU

96
Q

EU Wealth Function

A

Bernoulli suggests a logarithmic function
It has the diminishing marginal utility property:
log_10 of ⁡10=1, log_10⁡ of 100=2, log_10⁡ of 1,000=3

By cardinality, this means the utility difference between $10 and $100 is the same as the utility difference between $100 and $1,000.

97
Q

Futility of Utility

A

log base k will not fit all preferences for money – k determined by preferences between (1, 10, 100, 1,000, etc.) – and just one inconsistency falsifies the utility function.

98
Q

Axiomatic Approach to EU

A

EU Maximizers will follow rules of:

  1. Completeness
  2. Transitivity
  3. Continuity
  4. Independence of Irrelevant Alternatives (Independence Axiom)
99
Q

Graphing Riskiness (EU)

A

x-axis = wealth
y-axis = utility

Risk Neutral = linear (equivalent to maximizing EV)
Risk Aversive = logarithmic (diminishing marginal utility)
Risk Loving = exponential (increasing marginal utility)

100
Q

Rabin’s Critique of Diminishing Marginal Utility

A

Diminishing Marginal Utility means that under EU, rejecting small bets with slightly positive EV necessitates rejecting large bets with immensely positive EV

The problem is that a Risk Averse EU Maximizer must have Diminishing Marginal Utility of Wealth, and even seemingly moderate Diminishing Marginal Utility means that if small stake, positive EV bets are rejected, large stake, immensely positive or infinite EV bets must also be rejected.

101
Q

Certainty Effect

A

1% increase of positive gain from 99% to 100% is much more valuable than the 1% increase from 98% to 99%.

EU treats each percent of probability equally (linear in probability)!

102
Q

Prospect Theory Reflection Effect (Fourfold Pattern of RIsk)

A
  1. Risk Averse over high probability gains (Problems 3 and 7)
  2. Risk Loving over low probability gains (Problems 4 and 8)
  3. Risk Loving over high probability losses (Problems 3’ and 7’)
  4. Risk Averse over low probability losses (Problems 4’ and 8’)
103
Q

Isolation Effect

A

People tend to disregard components/branches that lotteries share and focus on the components/branches that distinguish them.

A single-stage lottery under EU is equivalent to a multi-stage lottery if the final outcomes and probabilities are the same.

104
Q

Problems with EU

A
  1. Rabin’s Critique of Diminishing Marginal Utility of Wealth
  2. Allais Paradox/Certainty Effect
  3. Common Ratio Effect
  4. Reflection Effect
  5. Isolation Effect
  6. Wealth Changes, not Final States
105
Q

Prospect Theory Value Function Graph (v(x))

A
  1. Should not depend on wealth 𝑤, just outcomes 𝑥
  2. Should incorporate Loss Aversion
  3. Should display Diminishing Sensitivity: the first dollar gained or lost should impact value MORE than the second dollar, etc.

Result: DMU for positive part, IMU for negative part, and an origin of (0,0) that represents current wealth or expectations.

106
Q

Prospect Theory 𝜋(p) graphed

A
  1. Looks like middle of an x^3 function (rapid increase for first bit, slow upward sloping curve for middle, and rapid increase for last .2)
  2. 𝜋(0)=0 and 𝜋(1)=1
  3. Overweight small probabilities and underweight large ones
  4. Certainty Effect:
    𝜋(1)−𝜋(.95)>𝜋(.55)−𝜋(.5)
  5. Common Ratio Effect:
    𝜋(.05)−𝜋(0)>𝜋(.55)−𝜋(.5)
107
Q

First Order Stochastic Dominate (FOSD)

A

Definition: If for ALL monetary outcomes 𝑥, 𝐿 gives an equal or higher probability than 𝐿′ of receiving something greater than 𝑥.

Normative Rule: You should not choose the dominated lottery 𝐿′.

108
Q

Ellsberg Paradox

A

Two jars with 100 balls each. Jar A has 50 black and 50 red balls. Jar B has red and black balls in unknown amounts. Pick the right ball, get $100.

Most people prefer jar A.

Demonstrates Ambiguity Aversion.

109
Q

What EU axiom does regret theory violate?

A

Transitivity

Behavioral Economics And Psychology (2 decks)

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