binaryRL (version 0.9.0)

func_gamma: Function: Utility Function

Description

This function represents an exponent used in calculating utility from reward. Its application varies depending on the specific model:

• Stevens' Power Law: Here, utility is calculated by raising the reward to the power of gamma. This describes how the subjective value (utility) of a reward changes non-linearly with its objective magnitude.

• Kahneman's Prospect Theory: This theory applies exponents differently for gains and losses, and introduces a loss aversion coefficient:

  • For positive rewards (gains), utility is the reward raised to the power of gamma[1].

  • For negative rewards (losses), utility is calculated by first multiplying the reward by beta, and then raising this product to the power of gamma[2]. Here, beta acts as a loss aversion parameter, accounting for the greater psychological impact of losses compared to equivalent gains.

Usage

func_gamma(
  i,
  L_freq,
  R_freq,
  L_pick,
  R_pick,
  L_value,
  R_value,
  var1 = NA,
  var2 = NA,
  value,
  utility,
  reward,
  occurrence,
  gamma = 1,
  alpha,
  beta
)

Value

Discount rate and utility

Arguments

i

The current row number.

L_freq

The frequency of left option appearance

R_freq

The frequency of right option appearance

L_pick

The number of times left option was picked

R_pick

The number of times left option was picked

L_value

The value of the left option

R_value

The value of the right option

var1

[character] Column name of extra variable 1. If your model uses more than just reward and expected value, and you need other information, such as whether the choice frame is Gain or Loss, then you can input the 'Frame' column as var1 into the model.

default: var1 = "Extra_Var1"

var2

[character] Column name of extra variable 2. If one additional variable, var1, does not meet your needs, you can add another additional variable, var2, into your model.

default: var2 = "Extra_Var2"

value

The expected value of the stimulus in the subject's mind at this point in time.

utility

The subjective value that the subject assigns to the objective reward.

reward

The objective reward received by the subject after selecting a stimulus.

occurrence

The number of times the same stimulus has been chosen.

gamma

[vector] This parameter represents the exponent in utility functions, specifically:

• Stevens' Power Law: Utility is modeled as: $$U(R) = {R}^{\gamma}$$

• Kahneman's Prospect Theory: This exponent is applied differently based on the sign of the reward: $$U(R) = \begin{cases} R^{\gamma_{1}}, & R > 0 \\ \beta \cdot R^{\gamma_{2}}, & R < 0 \end{cases}$$

alpha

[vector] Extra parameters that may be used in functions.

beta

[vector] Extra parameters that may be used in functions.

Examples

if (FALSE) {
func_gamma <- function(
  # Trial number
  i,
  # Number of times this option has appeared
  L_freq,
  R_freq,
  # Number of times this option has been chosen
  L_pick,
  R_pick,
  # Current value of this option
  L_value,
  R_value,
  # Extra variables
  var1 = NA,
  var2 = NA,
  
  # Expected value for this stimulus
  value,
  # Subjective utility
  utility,
  # Reward observed after choice
  reward,
  # Occurrence count for this stimulus
  occurrence,
  
  # Free Parameter
  gamma = 1,
  # Extra parameters
  alpha,
  beta
){
############################## [ Utility ] ##################################
  if (length(gamma) == 1) {
    gamma <- as.numeric(gamma)
    utility <- sign(reward) * (abs(reward) ^ gamma)
  }
############################### [ Error ] ###################################
  else {
    utility <- "ERROR" 
  }
  return(list(gamma, utility))
}
}