ExpectedUtility{T <: Real} <: UtilityModel

A model object for expected utility theory

Fields

• α: utility curvature
• θ: temperature or decisional consistency

Constructors

ExpectedUtility(; α = .80, θ = 1.0)

ExpectedUtility(α, θ)

Example

using UtilityModels

gamble1 = Gamble(; 
    p = [.25, .25, .50], 
    v = [44, 40, 5]
)

gamble2 = Gamble(; 
    p = [.25, .25, .50], 
    v = [98, 10, 5]
)

gambles = [gamble1,gamble2]

mean.(model, gambles)
std.(model, gambles)

model = ExpectedUtility(; α = .80, θ = 1.0)

pdf(model, gambles, 1)

logpdf(model, gambles, 1)

Gamble{T <: Real}

A gamble object with probability vector p and outcome vector v.

Fields

• p: probability vector
• v: outcome vector

Constructors

Gamble(; p = [0.5, 0.5], v = [10.0, 0.0])

Gamble(p, v)

ProspectTheory{T <: Real} <: AbstractProspectTheory

A model object for cummulative prospect theory. By default, parameters for utility curvature and probability weigting are equal gains and losses.

Fields

• α = .80: utility curvature for gains
• β = α: utility curvature for losses
• γg = .70: probability weighting parameter for gains
• γl = γg: probability weighting parameter for losses
• λ = 2.25: loss aversion parameter
• θ: temperature or decisional consistency

Constructors

ProspectTheory(; α = 0.80, β = α, γg = 0.70, γl = γg, λ = 2.25, θ = 1.0)

ProspectTheory(α, β, γg, γl, λ, θ)

Example

using UtilityModels

gamble1 = Gamble(; 
    p = [.25, .25, .50], 
    v = [44, 40, 5]
)

gamble2 = Gamble(; 
    p = [.25, .25, .50], 
    v = [98, 10, 5]
)

gambles = [gamble1,gamble2]

mean.(model, gambles)
std.(model, gambles)

model = ProspectTheory(; 
    α = 0.80, 
    γg = 0.70, 
    λ = 2.25, 
    θ = 1.0
)

pdf(model, gambles, 1)

logpdf(model, gambles, 1)

References

Fennema, H., & Wakker, P. (1997). Original and cumulative prospect theory: A discussion of empirical differences. Journal of Behavioral Decision Making, 10(1), 53-64.

Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and uncertainty, 5(4), 297-323.

TAX{T <: Real} <: AbstractTAX

A model object for transfer of attention exchange.

Fields

• δ = 1.0: transfer of attention parameter
• γ = 1.0: probability weighting parameter
• β = .70: utility curvature
• θ: temperature or decisional consistency

Constructors

TAX(; δ = -1.0, β = 1.0, γ = 0.70, θ = 1.0)

TAX(δ, γ, β, θ)

Example

using UtilityModels

gamble1 = Gamble(; 
    p = [.25, .25, .50], 
    v = [44, 40, 5]
)

gamble2 = Gamble(; 
    p = [.25, .25, .50], 
    v = [98, 10, 5]
)

gambles = [gamble1,gamble2]

mean.(model, gambles)
std.(model, gambles)

model = TAX(; 
    δ = -1.0, 
    β = 1.0, 
    γ = 0.70, 
    θ = 1.0
)

pdf(model, gambles, 1)

logpdf(model, gambles, 1)

References

Birnbaum, M. H., & Chavez, A. (1997). Tests of theories of decision making: Violations of branch independence and distribution independence. Organizational Behavior and Human Decision Processes, 71(2), 161-194. Birnbaum, M. H. (2008). New paradoxes of risky decision making. Psychological Review, 115(2), 463.

UtilityModel <: DiscreteMultivariateDistribution

UtilityModel is an abstract type for utility-based models ````

ValenceExpectancy{T <: Real} <: AbstractValenceExpectancy

A model object for expected utility theory

Fields

• υ: a vector of expected utilities
• Δ: learning rate where Δ ∈ [0,1]
• α: utility shape parameter where α > 0
• λ: loss aversion where λ > 0
• c: temperature

Constructors

ValenceExpectancy(; n_options, Δ, α = 0.80, λ, c)

ValenceExpectancy(Δ, α, λ, c)

logpdf(model::UtilityModel, gambles::Vector{<:Gamble}, choice::Int)

Computes the choice log probability for a vector of gambles.

Arguments

• model::UtilityModel: a utility model
• gambles::Vector{<:Gamble}: a vector of gambles representing a choice set
• choice_idxs::Vector{<:Int}: indices for the chosen gambles

pdf(model::UtilityModel, gambles::Vector{<:Gamble}, choice::Int)

Computes the choice probability for a vector of gambles.

Arguments

• model::UtilityModel: a utility model
• gambles::Vector{<:Gamble}: a vector of gambles representing a choice set
• choice_idxs::Vector{<:Int}: indices for the chosen gambles

mean(model::UtilityModel, gamble::Gamble)

Computes mean or expected utility

Arguments

• model::UtilityModel: a model M <: UtilityModel
• gamble::Gamble: a gamble object

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mean(model::AbstractTAX, gamble::Gamble)

Computes mean utility for the TAX model

Arguments

• model::AbstractTAX: a model M <: UtilityModel
• gamble::Gamble: a gamble object

std(model::UtilityModel, gamble::Gamble)

Computes the standard deviation of the gamble

Arguments

• model::UtilityMode: a model M <: UtilityModel
• gamble::Gamble: a gamble object

var(model::UtilityModel, gamble::Gamble)

Computes the variance of the gamble

Arguments

• model::UtilityModel: a utility model
• gamble::Gamble: a gamble object

compute_utility(model::ExpectedUtility, gamble::Gamble)

Computes utility of gamble outcomes according to expected utility theory.

Arguments

• model::ExpectedUtility: a model object for prospect theory
• gamble::Gamble: a gamble object

compute_utility(model::AbstractProspectTheory, gamble)

Computes utility of gamble outcomes according to prospect theory

Arguments

• model::AbstractProspectTheory: a model object for prospect theory
• gamble: a gamble object

compute_utility(model::AbstractTAX, gamble)

Computes utility of gamble outcomes according to TAX

Arguments

• model::AbstractTAX: a model object for TAX
• gamble: a gamble object

compute_utility(model::ValenceExpectancy, outcomes::Vector)

compute_utility computes utility of gamble outcomes according to expected utility theory

• model: a model object for prospect theory
• outcomes: observed outcomes of decisions