Behavioral Economics Guide

Key features:
1. Reference dependence: Utility is defined over gains and losses, not absolute wealth
2. Loss aversion: lambda ≈ 2.25 (losses hurt ~2.25x more than equivalent gains)
3. Diminishing sensitivity: Marginal impact decreases as you move away from reference
4. Probability weighting: Overweight small probabilities, underweight large ones

Value function:
v(x) = x^alpha            if x >= 0  (alpha ≈ 0.88)
v(x) = -lambda * (-x)^beta if x < 0  (beta ≈ 0.88, lambda ≈ 2.25)

Probability weighting function (Prelec, 1998):
w(p) = exp(-(-ln(p))^alpha)   (alpha ≈ 0.65 for gains, 0.69 for losses)

# Example: Dictator Game implementation with oTree
# oTree is the standard platform for behavioral economics experiments

# models.py
class Player(BasePlayer):
    dictator_give = models.CurrencyField(
        min=0, max=100,
        label="How much do you want to give to the other participant?"
    )

# pages.py
class Decision(Page):
    form_model = 'player'
    form_fields = ['dictator_give']

    def vars_for_template(self):
        return {'endowment': 100}

class Results(Page):
    def vars_for_template(self):
        return {
            'kept': 100 - self.player.dictator_give,
            'given': self.player.dictator_give
        }

Design checklist for a behavioral field experiment:

1. RESEARCH QUESTION
   "Does changing the default retirement contribution rate from 3% to 6%
   increase average savings?"

2. TREATMENT ARMS
   - Control: Default contribution = 3% (status quo)
   - Treatment 1: Default contribution = 6% (higher default)
   - Treatment 2: Default contribution = 6% + active choice prompt

3. RANDOMIZATION
   - Unit: Individual employees
   - Method: Stratified randomization by age, salary, tenure
   - Balance checks: t-tests on observables across treatment arms

4. SAMPLE SIZE
   - Power calculation: N = 1,200 per arm (power=0.80, MDE=2pp,
     alpha=0.05, ICC adjusted for clustering by department)

5. OUTCOME MEASURES
   - Primary: Contribution rate at 6 months
   - Secondary: Total savings at 12 months, opt-out rate
   - Administrative data (no survey needed)

6. PRE-REGISTRATION
   - Register on AEA RCT Registry before treatment assignment

# Example: Willingness-to-Pay (WTP) elicitation using BDM mechanism
# Becker-DeGroot-Marschak procedure

import numpy as np

def bdm_auction(stated_wtp, item_cost_range=(0, 20)):
    """
    Becker-DeGroot-Marschak incentive-compatible mechanism.
    Random price drawn; participant buys if WTP >= price.
    """
    random_price = np.random.uniform(*item_cost_range)
    buys = stated_wtp >= random_price
    payment = random_price if buys else 0
    return {
        "stated_wtp": stated_wtp,
        "random_price": round(random_price, 2),
        "purchased": buys,
        "payment": round(payment, 2)
    }

# This is incentive-compatible: truthfully reporting WTP is optimal
# because the price is determined independently of the stated WTP

# Estimating discount factors from multiple price list (MPL) choices

def estimate_discount_factor(choices, amounts, delays):
    """
    Estimate quasi-hyperbolic discounting parameters (beta, delta)
    from a series of smaller-sooner vs. larger-later choices.

    beta: present bias (< 1 means present-biased)
    delta: long-run discount factor (per period)
    """
    from scipy.optimize import minimize

    def neg_log_likelihood(params):
        beta, delta = params
        ll = 0
        for choice, (ss, ll_amt), (t_ss, t_ll) in zip(choices, amounts, delays):
            # Discounted utility of each option
            if t_ss == 0:
                u_ss = ss  # No discounting for immediate
                u_ll = beta * (delta ** t_ll) * ll_amt
            else:
                u_ss = beta * (delta ** t_ss) * ss
                u_ll = beta * (delta ** t_ll) * ll_amt

            p_ll = 1 / (1 + np.exp(-(u_ll - u_ss)))  # Logit
            ll += choice * np.log(p_ll + 1e-10) + (1-choice) * np.log(1-p_ll + 1e-10)
        return -ll

    result = minimize(neg_log_likelihood, [0.9, 0.95],
                      bounds=[(0.01, 1.5), (0.8, 1.0)])
    return {"beta": result.x[0], "delta": result.x[1]}