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203 | def prospect_theory(
name="Prospect Theory",
choice_temperature=0.1,
value_alpha=0.88,
value_beta=0.88,
value_lambda=2.25,
probability_alpha=0.61,
probability_beta=0.69,
resolution=10,
minimum_value=-1,
maximum_value=1,
):
"""
Parameters from
D. Kahneman, A. Tversky, Prospect theory: An analysis of decision under risk.
Econometrica 47, 263–292 (1979). doi:10.2307/1914185
Power value function according to:
- A. Tversky, D. Kahneman, Advances in prospect theory: Cumulative representation of
uncertainty. J. Risk Uncertain. 5, 297–323 (1992). doi:10.1007/BF00122574
- I. Gilboa, Expected utility with purely subjective non-additive probabilities.
J. Math. Econ. 16, 65–88 (1987). doi:10.1016/0304-4068(87)90022-X
- D. Schmeidler, Subjective probability and expected utility without additivity.
Econometrica 57, 571 (1989). doi:10.2307/1911053
Probability function according to:
A. Tversky, D. Kahneman, Advances in prospect theory: Cumulative representation of
uncertainty. J. Risk Uncertain. 5, 297–323 (1992). doi:10.1007/BF00122574
"""
params = dict(
choice_temperature=choice_temperature,
value_alpha=value_alpha,
value_beta=value_beta,
value_lambda=value_lambda,
probability_alpha=probability_alpha,
probability_beta=probability_beta,
resolution=resolution,
minimum_value=minimum_value,
maximum_value=maximum_value,
name=name,
)
variables = get_variables(
minimum_value=minimum_value, maximum_value=maximum_value, resolution=resolution
)
def run(
conditions: Union[pd.DataFrame, np.ndarray, np.recarray],
added_noise=0.01,
random_state: Optional[int] = None,
):
rng = np.random.default_rng(random_state)
X = np.array(conditions)
Y = np.zeros((X.shape[0], 1))
for idx, x in enumerate(X):
# power value function according to:
# A. Tversky, D. Kahneman, Advances in prospect theory: Cumulative representation of
# uncertainty. J. Risk Uncertain. 5, 297–323 (1992). doi:10.1007/BF00122574
# I. Gilboa, Expected utility with purely subjective non-additive probabilities.
# J. Math. Econ. 16, 65–88 (1987). doi:10.1016/0304-4068(87)90022-X
# D. Schmeidler, Subjective probability and expected utility without additivity.
# Econometrica 57, 571 (1989). doi:10.2307/1911053
# compute value of option A
if x[0] > 0:
value_A = x[0] ** value_alpha
else:
value_A = -value_lambda * (-x[0]) ** (value_beta)
# compute value of option B
if x[2] > 0:
value_B = x[2] ** value_alpha
else:
value_B = -value_lambda * (-x[2]) ** (value_beta)
# probability function according to:
# A. Tversky, D. Kahneman, Advances in prospect theory: Cumulative representation of
# uncertainty. J. Risk Uncertain. 5, 297–323 (1992). doi:10.1007/BF00122574
# compute probability of option A
if x[0] >= 0:
coefficient = probability_alpha
else:
coefficient = probability_beta
probability_a = x[1] ** coefficient / (
x[1] ** coefficient + (1 - x[1]) ** coefficient
) ** (1 / coefficient)
# compute probability of option B
if x[2] >= 0:
coefficient = probability_alpha
else:
coefficient = probability_beta
probability_b = x[3] ** coefficient / (
x[3] ** coefficient + (1 - x[3]) ** coefficient
) ** (1 / coefficient)
expected_value_A = value_A * probability_a + rng.normal(0, added_noise)
expected_value_B = value_B * probability_b + rng.normal(0, added_noise)
# compute probability of choosing option A
p_choose_A = np.exp(expected_value_A / choice_temperature) / (
np.exp(expected_value_A / choice_temperature)
+ np.exp(expected_value_B / choice_temperature)
)
Y[idx] = p_choose_A
experiment_data = pd.DataFrame(conditions)
experiment_data.columns = [v.name for v in variables.independent_variables]
experiment_data[variables.dependent_variables[0].name] = Y
return experiment_data
ground_truth = partial(run, added_noise=0.0)
def domain():
v_a = variables.independent_variables[0].allowed_values
p_a = variables.independent_variables[1].allowed_values
v_b = variables.independent_variables[2].allowed_values
p_b = variables.independent_variables[3].allowed_values
X = np.array(np.meshgrid(v_a, p_a, v_b, p_b)).T.reshape(-1, 4)
return X
def plotter(model=None):
import matplotlib.colors as mcolors
import matplotlib.pyplot as plt
v_a_list = [-0.5, 0.5, 1]
p_a = np.linspace(0, 1, 100)
v_b = 0.5
p_b = 0.5
for idx, v_a in enumerate(v_a_list):
X = np.zeros((len(p_a), 4))
X[:, 0] = v_a
X[:, 1] = p_a
X[:, 2] = v_b
X[:, 3] = p_b
y = ground_truth(X)
colors = mcolors.TABLEAU_COLORS
col_keys = list(colors.keys())
plt.plot(
p_a, y, label=f"$V(A) = {v_a}$ (Original)", c=colors[col_keys[idx]]
)
if model is not None:
y = model.predict(X)
plt.plot(
p_a,
y,
label=f"$V(A) = {v_a}$ (Recovered)",
c=colors[col_keys[idx]],
linestyle="--",
)
x_limit = [0, variables.independent_variables[1].value_range[1]]
y_limit = [0, 1]
x_label = "Probability of Choosing Option A"
y_label = "Probability of Obtaining V(A)"
plt.xlim(x_limit)
plt.ylim(y_limit)
plt.xlabel(x_label, fontsize="large")
plt.ylabel(y_label, fontsize="large")
plt.legend(loc=2, fontsize="medium")
plt.title(name, fontsize="x-large")
collection = SyntheticExperimentCollection(
name=name,
description=prospect_theory.__doc__,
params=params,
variables=variables,
domain=domain,
run=run,
ground_truth=ground_truth,
plotter=plotter,
factory_function=prospect_theory,
)
return collection
|