Bounded Rationality and Rule of Thumb Models

• Different approaches to boundedly rational models in economics
  • Psychology-economics style: behavioral models where consumers behave irrationally and firms exploit them
  • Rule of thumb approach: write down models resembling actual consumer behavior rather than complex rational models
• Critique of rational modeling approach
  • Complex 8-page mathematical arguments for top journal publication
  • Full rationality assumptions often unbelievable
  • Rational modeling can still involve "cheating" through assumption selection
  • Sociology of economics: complicated calculations needed to show academic accomplishment

Smallwood and Conlisk Model (Classic Rule of Thumb Example)

• Research question: Do superior products win out in markets with imperfect information?
• Cereal box example: consumers face complex information processing
  • Only tasted small fraction of available cereals
  • Must infer quality from limited information (prices, others' purchases, advertising, shelf placement)
  • Rational approach would require prior over century's worth of cereal purchases and network effects
• Model assumptions:
  • Products differ in quality (breakdown probability BK)
  • Consumers continue buying same product until breakdown occurs
  • After breakdown, buy product K with probability MK(T)^σ (market share raised to sigma power)
• Sigma parameter interpretations:
  • σ = 0: random selection from available products
  • σ = 1: proportional to market share (watching one person ahead)
  • σ > 1: explicit reasoning about popularity correlation with quality
  • σ → ∞: always buy most popular brand

Smallwood-Conlisk Results

• Main theorem: If σ = 1, most popular product dominates in T → ∞ limit
  • Product with smallest BK (highest quality) achieves MK(T) → 1
  • Best product takes over, inferior products die out
• σ < 1: All products remain active with positive market shares
  • Superior products have larger shares but don't reach monopoly
• σ > 1: Inferior products can dominate through initial popularity advantages
• Key insight: Consumers must be fairly naive (σ = 1) for market selection to work optimally
  • Put some weight on popularity but not too much

Banerjee-Fudenberg Extension (1995)

• More utility-framework approach to Smallwood-Conlisk
• Consumers receive utility with product-specific means and idiosyncratic preferences
• Period-specific quality differences (e.g., traffic routes, restaurant quality, insurance coverage)
• Product 1 better with probability P
• Consumer behavior:
  • Buy same product with probability 1-α (inertia)
  • With probability α, ask n friends about recent experiences
  • Choose product with better average utility among friends
• Results: Optimal social learning occurs when n is fairly small
  • When α close to 1 (frequent questioning), need 3-6 friends
  • When α small, asking 1 friend works well (similar to Smallwood-Conlisk σ=1)

Spiegler's Market for Quacks Model

• Extends word-of-mouth models to include firm pricing
• Application: health supplements/medications advertised online
• Model setup:
  • Large number of products giving good outcome with probability α
  • Outside option also gives good outcome with probability α at zero cost
  • Utility from product K: (1-PKT) with probability α, -PKT with probability (1-α)
• Consumer behavior: Ask one user of each product about experience, buy product giving highest utility if positive
• Results similar to Stahl price dispersion model
  • Mixed strategy equilibrium with price distributions
  • Price inversely related to product quality
  • High-quality products face more competition (more positive reviews), leading to lower prices
  • Low-quality products face less competition (fewer positive reviews), enabling higher prices

Journal Refereeing Process Model

• Academic publishing as rule of thumb application
• Paper quality has two dimensions:
  • Q: fundamental idea/insight (unchangeable)
  • R: craftsmanship quality (improvable through revision)
• Referee learning process:
  • Referees don't know true α (weight on Q) and Z (quality threshold)
  • Try to learn from experience with own papers and observed acceptances/rejections
• Overconfidence bias: Everyone thinks their papers are ε better than reality
• Dynamics lead to perpetual disequilibrium:
  • Referees set standards too high
  • Editors accept papers below referee recommendations to fill journals
  • Creates cognitive dissonance leading to preference for R over Q
• Empirical evidence: Publication times increased from 6-8 months (1970s) to 2-3 years (2000s)
  • Median time for top IO empirical papers: 7 years from job market to publication

Advertising Theory Overview

• Three main approaches to modeling advertising effects:
  1. Informational content: tells consumers about product existence, prices, attributes
  2. Signaling: signals quality through money-burning
  3. Preference manipulation: directly changes consumer preferences

Butters Model (1977) - Informational Advertising

• Setup: n firms selling identical goods, unit mass of identical consumers
• Consumers get utility V-P, firms have cost C
• Advertising technology: spending A(x) reaches fraction x of consumers
• Equilibrium features:
  • Price dispersion (similar to Stahl model)
  • Consumers buy from cheapest firm they heard about
  • Mixed strategy pricing: P = V for monopoly consumers, lower prices for competitive situations
• Key result: Advertising levels are socially efficient
  • Private return to reaching marginal consumer equals social return
  • Marginal benefit = (V-C) × Pr(consumer saw no other ad)
  • No distortion from business stealing or consumer surplus effects

Milgram-Roberts Model (1980s) - Signaling Advertising

• Two-quality products (high H, low L) with common prior
• Firms observe own quality, choose price P and advertising level A
• Consumers observe A, update beliefs about quality, make purchase decisions
• Profits depend on both true quality Q and perceived quality Q̂
• Separating equilibrium possible:
  • High-quality firms: high price + positive advertising
  • Low-quality firms: low price + zero advertising
• Requirements for equilibrium:
  • Repeat purchases must be important
  • Word-of-mouth learning effects must be small
• Advertising is pure money-burning but can be socially valuable through improved matching

Behavioral Advertising Model (Shapiro - Unpublished)

• Based on memory manipulation and confusion
• Psychological evidence: famous person experiments, orange juice taste tests
• Consumer types θ get benefit V with probability θ when consuming good
• Consumers have n prior experiences but recall only one for decision-making
• Two advertising mechanisms:
  1. Memory replacement: substitute fake memory for real one
  2. Memory priming: make positive memories more likely to be recalled
• Even with rational consumers aware of manipulation, firms may still advertise for information design reasons
• Advertising effectiveness depends on product quality (less beneficial for truly high-quality products)

Marketing Field Relationship

• Marketing departments have ~1000 professors in US with dedicated journals
• Citations in marketing papers: 6% to economics (up from historical levels)
• IO theory and empirical work heavily cited in marketing literature
• Substantial overlap in topics: pricing, demand estimation, advertising campaign effects