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autora.experiment_runner.synthetic.economics.expected_value_theory

expected_value_theory(name='Expected Value Theory', choice_temperature=0.1, value_lambda=0.5, resolution=10, minimum_value=-1, maximum_value=1)

Expected Value Theory

Parameters:

Name Type Description Default
name
'Expected Value Theory'
choice_temperature float
0.1
value_lambda float
0.5
resolution
10
minimum_value
-1
maximum_value
1
Source code in autora/experiment_runner/synthetic/economics/expected_value_theory.py 
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def expected_value_theory(
    name="Expected Value Theory",
    choice_temperature: float = 0.1,
    value_lambda: float = 0.5,
    resolution=10,
    minimum_value=-1,
    maximum_value=1,
):
    """
    Expected Value Theory

    Parameters:
        name:
        choice_temperature:
        value_lambda:
        resolution:
        minimum_value:
        maximum_value:
    """

    params = dict(
        name=name,
        minimum_value=minimum_value,
        maximum_value=maximum_value,
        resolution=resolution,
        choice_temperature=choice_temperature,
        value_lambda=value_lambda,
    )

    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: float = 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):
            value_A = value_lambda * x[0]
            value_B = value_lambda * x[2]

            probability_a = x[1]
            probability_b = x[3]

            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():
        X = np.array(
            np.meshgrid([x.allowed_values for x in variables.independent_variables])
        ).T.reshape(-1, 4)
        return X

    def plotter(model=None):
        import matplotlib.colors as mcolors
        import matplotlib.pyplot as plt

        v_a_list = [-1, 0.5, 1]
        v_b = 0.5
        p_b = 0.5
        p_a = np.linspace(0, 1, 100)

        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=expected_value_theory.__doc__,
        variables=variables,
        run=run,
        ground_truth=ground_truth,
        domain=domain,
        plotter=plotter,
        params=params,
        factory_function=expected_value_theory,
    )
    return collection