Key Concepts in Behavioral Economics and Decision-Making

Small-Scale vs. Large-Scale Risk Aversion

The core idea is to understand the differences between how small and large changes in wealth affect risky gambles.

Diminishing marginal utility (risk aversion) primarily applies to large-scale gambles. This is because the utility function is sufficiently concave over lifetime changes in wealth. This concavity results in a higher utility for taking a certain outcome than for taking a gamble, even if the gamble has a higher expected return.

However, for small-scale gambles, the utility function is locally linear, yielding almost risk-neutral behavior. For wealthy individuals, the utility function is very weakly concave, leading to an asymptotically linear curvature. Thus, diminishing marginal utility cannot explain the rejection of small gambles because risk aversion decreases (asymptotically to zero) as wealth increases.

Diminishing marginal utility requires that different wealth levels are determined by a single function.

Reference-Dependence Explanations

• What is evaluated in a reference-dependent way?
  • Daily income, prices, wages/consumption, and stock prices.
• What is the reference point?
  • Average daily income (goals), recent price expectations, adaptation/status quo of income, or the initial price of a stock.
• What feature of the value function explains the application?
  • Loss aversion, diminishing sensitivity, and non-linear probability weighting.

Inexperienced individuals are often driven by loss aversion and reference-dependence, which creates the endowment effect.

Experienced individuals are less prone to loss aversion and reference-dependence. They also make fewer mistakes and minimize biases/heuristics, leading to more rational, familiar, and efficient decision-making.

Prospect Theory Scenarios

What domain do the outcomes fall into? Positive, negative, or both?

• Positive Domain: Risk aversion dominates due to diminishing marginal utility.
• Negative Domain: Risk-loving behavior dominates due to diminishing sensitivity.
• Mixed Domain (Both): Loss aversion dominates.

Shocks to wealth can push an individual into either the positive or negative domain. A positive shock may cause an individual to exhibit less risk aversion as their wealth increases. The function becomes almost linear, inducing risk-neutral preferences. If the reference point adjusts to the shock, the original scenario repeats.

Non-Linear Probability Weighting

Individuals apply decision weights that assess the probabilities of outcomes differently. They perceive different magnitudes of change at different points on the probability weighting function.

• Individuals tend to overweight outcomes with small probabilities.
• Individuals often prefer certain outcomes over likely outcomes due to the underweighting of high probabilities and the certainty effect.

There are competing forces between risk aversion in the value function and the overweighting of probabilities.

Exponential and Hyperbolic Discounting

This concerns how future utilities are valued relative to the present. Consider the benefits and costs now versus the benefits and costs in the future.

• A present-biased person subjects costs and benefits experienced with any delay to a short-term discount factor (beta).
• An exponential discounter subjects future costs and benefits to a consistent delta discount factor, which measures impatience.

Naïve hyperbolic discounting: An individual is unaware of their present-biased preferences and believes their preferences will not change over time.

Sophisticated hyperbolic discounting: An individual is aware of their present-biased preferences and solves problems via backwards induction. For a sophisticated person, present bias may cause procrastination. However, their sophistication prevents them from delaying again, as they know it will lead to the worst outcome.

A richer, more complex choice set with better options can actually increase procrastination and strengthen the “status quo” effect, as people dislike having too many choices.

Projection Bias

No projection bias: An individual is fully aware that they will adapt and that their current state/preferences will change in the future.

Projection bias: An individual does not realize they will adapt and projects their current state/preferences into the future. This bias typically applies to durable goods, as non-durable goods do not yield utility far into the future.

Projection Bias vs. Hyperbolic Discounting:

• Hyperbolic discounting is about patience; being more patient leads to better realization of future costs/benefits.
• Projection bias is about changes in preferences over time; it involves recognizing that one's current state will not last forever.

Anticipatory Utility

Compare the instrumental utility with the belief utility. What is driving utility in each component? The addition of anticipatory utility gives insight into how individuals seek information under uncertain outcomes.

Check the concavity and weight of the anticipatory utility function:

• Concave: Information risk-averse.
• Convex: Information-seeking.

Heuristics and Biases

Judgment Heuristic

An informal algorithm that generates an approximate answer to a problem quickly. It is neither inherently good nor bad and can be used alongside perfect statistical and probability judgments. For example, when asked to determine which of two cities has a larger population, if a person only recognizes one city, they might choose that one as an approximation.

Representativeness Heuristic

People use similarity or representativeness as a proxy for probabilistic thinking. They evaluate probabilities by the degree to which A is representative of (similar to) B. For example, using a person's features to infer their likely occupation, even if there is no statistical relationship.

Availability Heuristic

People assess the frequency of a class or the probability of an event by the ease with which instances can be brought to mind. It’s easier to recall things that are more common or probable, driven by: 1) Rehearsal, and 2) Familiarity.

Anchoring and Adjustment Heuristic

People often answer a question by starting with a first-pass guess (an anchor) based on memory or the environment, and then adjusting that guess. For instance, if you know the odds of outcome A and want to estimate the odds of outcome B, you might start with the odds of A and adjust. The quality of the anchor relates to its correlation with the quantity being estimated, and the size of the adjustment must account for this relationship.

Constructing Preferences

Choice Overload

When there are too many options, people might revert to a safe default option or use a simple choice heuristic to make their decision.

Compromise Effect

When unsure about what they want, people tend to choose a compromise (middle) option. This is a common response to complex, conflicted choices.

Mental Accounting

The set of cognitive operations used by individuals and households to organize, evaluate, and keep track of financial activities. People separate their money into different mental accounts, and money in these accounts is treated differently (it is not perfectly fungible). Accounts are often constrained by budgets. This can help make better financial decisions, control spending, and attach value to consumption goods.

Coherent Arbitrariness

Preferences can be influenced by irrelevant cues, but once people state a preference, their related preferences are consistent with it. People don’t seem to have clear, pre-existing preferences and often construct them on the spot. In an economic environment, cues include the Price Effect and the Context Effect.

Context Effects

People's choices depend on the other options in the choice set; their preferences are a function of the menu. This can lead to violations of rational choice, as irrelevant alternatives can influence the ranking of choices. When an alternative choice is presented, how are we weighting the factors?

Price Effects

Market prices can partly determine people’s preferences. This is the opposite of standard economic theory, where preferences are supposed to determine market prices.

Narrow vs. Broad Bracketing

• Narrow Bracketing: Leads to risk-averse behavior.
• Broad Bracketing: Leads to risk-neutral behavior (or acceptance of more risk).

One must look at the probabilities of making a loss versus a gain and how individuals incorporate the outcome into their utility. When already taking on significant risk, agents are expected to be risk-neutral toward gambles with small stakes.

Interpreting Sequences of Outcomes

Gambler's Fallacy

The false belief that in a sequence of independent draws, an outcome that hasn’t occurred for a while is more likely to occur next. This stems from knowing the true distribution of outcomes and incorrectly assuming it must hold for a small sample.

Hot-Hand Fallacy

The exaggerated belief that a person’s performance varies systematically over the short run. This occurs when one does not know the sequence of outcomes is independent and incorrectly infers that the distribution of outcomes changes for a small sample.

• The Gambler's Fallacy underestimates probability and leads to mispredictions.
• The Hot-Hand Fallacy overestimates probability and leads to over-inference of skill or ability.

Belief in the law of small numbers: The false belief that small samples must reflect the proportions of their underlying probabilities. This can be modeled using a quasi-Bayesian approach where individuals follow Bayes' rule but mistakenly assume draws are made without replacement.

Updating Beliefs with New Information

People use intuitive shortcuts to make judgments of likelihood. By focusing on an aspect of a situation that seems most relevant, they ignore other relevant aspects, leading to systematically incorrect likelihood estimates.

Base-Rate Neglect

Ignoring or underweighting the base rate of an event when judging its likelihood, especially when presented with new information. A quasi-Bayesian approach might assume a person’s prior beliefs put an equal probability on all possible baseline outcomes (e.g., Pr(p)=50%).

Confirmatory Bias

The tendency to misinterpret ambiguous evidence as confirming a current hypothesis. Suppose there are two hypotheses, A and B. If an individual's current belief is that A is more than 50% likely to be true, they will always interpret a signal supporting A ('a') correctly, but with some probability (p), they will misinterpret a signal supporting B ('b') as being 'a'.

• The variable p measures the extent of confirmatory bias.
• If p=0, the person updates beliefs in a rational Bayesian way.
• If p=1, it represents total confirmatory bias, where all new information is misread to support current beliefs.

Social Preferences

Distributional Preferences

Preferences that can be represented in terms of the amount of money or material resources people get.

[Insert Formula]

• Rho=sigma=0: Self-interested
• Rho=1, sigma=0: Rawlsian
• Rho=sigma=1/2: Utilitarian
• 1>rho>sigma>0: Social-Welfare Preferences
• 1>rho>0>sigma: Difference Aversion (or inequality aversion)
• Rho>1>0>sigma: Difference Phobia
• 0>rho>sigma: Competitive

[Insert FS model]

To determine equilibria under distributional preferences:

1. Compute the utility of the outcome.
2. Check the utility if Player 1 deviates.
3. Check the utility if Player 2 deviates.

Face-Saving Concerns

The motivation to avoid unfavorable judgments by others. If there is uncertainty about whether a selfish action will help or hurt another person, it provides an excuse to be selfish. When the benefit to the other person is clear, one might feel an obligation to help. There is clear evidence that people want to save face in front of themselves, not just others.

Intentions-Based Preferences (Reciprocity)

People like to treat others as others have treated them. People’s feelings about social allocations depend on how those allocations came about. A player cares about the intentions of the other player and tries to reciprocate those intentions.

Rabin's Model of Fairness

This model includes:

1. Exogenously given material payoffs.
2. Psychological payoffs based on impressions of fairness and unfairness.

People are willing to sacrifice their own payoff to help those they think have been kind and to punish those they think have been unkind. A fairness equilibrium is a situation where each player maximizes their utility, and their beliefs about the other player are correct.

Behavioral Game Theory

Identify whether synergistic or congestion effects are present. A synergistic effect has a large impact on the Nash Equilibrium (NE), while a congestion effect has a small impact.

Dominance Thinking

Determine the maximum (or minimum) guess and compute the target. Update the range with the new maximum (or minimum). A step-1 dominance player will play the optimal choice (the average of the range).

Information Projection

The typical person acts as if the information they currently have is available to others or in other situations, even when it’s clearly not.

Hindsight Bias

When a person receives information, they underestimate its importance in shaping beliefs when asked what they believed before knowing it. Hindsight bias is a manifestation of information projection: people project their current information onto earlier selves and onto others.

Curse of Knowledge

Those who know a piece of information cannot accurately predict or understand the behavior of those who do not have it.

The Winner’s Curse

In common-value auctions, bidders often overbid, leading the winner to make a loss. Because of the winner’s curse, the Nash equilibrium is to bid more conservatively.

Cursed Equilibrium

Each player correctly anticipates the distribution of play by others and maximizes utility given their (cursed) beliefs. A fully cursed player thinks the other player’s action doesn’t depend on their private information at all. A cursed bidder underappreciates that another bidder is more likely to bid low when their information indicates a low valuation, so they underappreciate the extent to which winning the auction is bad news. Cursedness can increase the amount of trade in markets with asymmetric information.

Public Policy Applications

Libertarian Paternalism

Policies that significantly help individuals with a specific failure, but do so without much reduction in anyone’s freedom to choose.

Asymmetric Paternalism

Policies that significantly help individuals with a specific failure and do not significantly hurt individuals whose behavior is optimal.

Robust Paternalism

Policies that produce a net social benefit, taking into account both consumers who are subject to a specific failure and consumers who optimize.