README.md
In dmi3kno/deals: Dealing with uncertainty. The choice is yours!
deals 
The purpose of deals is to faclitiate operations with and presentation
of decisions under uncertainty.
Installation
You can install the released version of deals from
Github with:
remotes::install_github("dmi3kno/deals")
Example
This is a basic example which shows you how to solve a common problem:
library(deals)
library(magrittr)
## basic example code
Transparent deals
Leland, Schneider, & Wilcox (2019) introduced definition of “transparent
frames” for decisions under uncertainty (hereafter, “deals”). In this
package a deal is a list of two dataframes, each with two columns p
(probability of a given outcome) and x (the outcome itself). Decision
maker is offered a choice between two uncertain prospects and can choose
one of them.
# Allais paradox
a1 <- list(
data.frame(
x=c(5e5),
p=c(1),
stringsAsFactors = FALSE),
data.frame(
x=c(2.5e6, 5e5, 0),
p=c(0.1, 0.89, 0.01),
stringsAsFactors = FALSE)
)
a1 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :------ | :----------------- | :-- | :-------- | :-------------------- |
| G1: | 500,000 | with probability 1 | G2: | 2,500,000 | with probability 0.10 |
| | | | | 500,000 | with probability 0.89 |
| | | | | 0 | with probability 0.01 |
deal_is_transparent(a1)
#> [1] FALSE
deal_make_transparent(a1) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :------ | :-------------------- | :-- | :-------- | :-------------------- |
| G1: | 500,000 | with probability 0.89 | G2: | 500,000 | with probability 0.89 |
| | 500,000 | with probability 0.10 | | 2,500,000 | with probability 0.10 |
| | 500,000 | with probability 0.01 | | 0 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a1))
#> [1] TRUE
a2 <- list(
data.frame(
x=c(5e5,0),
p=c(0.11,0.89),
stringsAsFactors = FALSE),
data.frame(
x=c(2.5e6,0),
p=c(0.10,0.90),
stringsAsFactors = FALSE)
)
a2 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :------ | :-------------------- | :-- | :-------- | :------------------- |
| G1: | 500,000 | with probability 0.11 | G2: | 2,500,000 | with probability 0.1 |
| | 0 | with probability 0.89 | | 0 | with probability 0.9 |
deal_is_transparent(a2)
#> [1] FALSE
deal_make_transparent(a2) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :------ | :-------------------- | :-- | :-------- | :-------------------- |
| G1: | 0 | with probability 0.89 | G2: | 0 | with probability 0.89 |
| | 500,000 | with probability 0.10 | | 2,500,000 | with probability 0.10 |
| | 500,000 | with probability 0.01 | | 0 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a2))
#> [1] TRUE
a3 <- list(
data.frame(
x=c(0, 45, 30, -15, -15),
p=c(0.9, 0.06, 0.01, 0.01, 0.02),
stringsAsFactors = FALSE),
data.frame(
x=c(0, 45, 45, -10, -15),
p=c(0.9, 0.06, 0.01, 0.01, 0.02),
stringsAsFactors = FALSE)
)
a3 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :--- | :-------------------- | :-- | :--- | :-------------------- |
| G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 |
| | 45 | with probability 0.06 | | 45 | with probability 0.06 |
| | 30 | with probability 0.01 | | 45 | with probability 0.01 |
| | -15 | with probability 0.01 | | -10 | with probability 0.01 |
| | -15 | with probability 0.02 | | -15 | with probability 0.02 |
# this one is transparent
deal_is_transparent(a3)
#> [1] TRUE
deal_make_transparent(a3) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :--- | :-------------------- | :-- | :--- | :-------------------- |
| G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 |
| | 45 | with probability 0.06 | | 45 | with probability 0.06 |
| | 30 | with probability 0.01 | | 45 | with probability 0.01 |
| | -15 | with probability 0.01 | | -10 | with probability 0.01 |
| | -15 | with probability 0.02 | | -15 | with probability 0.02 |
deal_is_transparent(deal_make_transparent(a3))
#> [1] TRUE
a4 <- list(
data.frame(
x=c(0, 45, 30, -15),
p=c(0.9, 0.06, 0.01, 0.03),
stringsAsFactors = FALSE),
data.frame(
x=c(0, 45, -10, -15),
p=c(0.9, 0.07, 0.01, 0.02),
stringsAsFactors = FALSE)
)
a4 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :--- | :-------------------- | :-- | :--- | :-------------------- |
| G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 |
| | 45 | with probability 0.06 | | 45 | with probability 0.07 |
| | 30 | with probability 0.01 | | -10 | with probability 0.01 |
| | -15 | with probability 0.03 | | -15 | with probability 0.02 |
deal_is_transparent(a4)
#> [1] FALSE
deal_make_transparent(a4) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :--- | :-------------------- | :-- | :--- | :-------------------- |
| G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 |
| | 45 | with probability 0.06 | | 45 | with probability 0.06 |
| | -15 | with probability 0.02 | | -15 | with probability 0.02 |
| | 30 | with probability 0.01 | | 45 | with probability 0.01 |
| | 0 | with probability 0.00 | | 0 | with probability 0.00 |
| | -15 | with probability 0.01 | | -10 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a4))
#> [1] TRUE
a5 <- list(
data.frame(
x=c(2500, 2400, 0),
p=c(0.33, 0.66, 0.01),
stringsAsFactors = FALSE),
data.frame(
x=c(2400, 2400, 2400),
p=c(0.33, 0.66, 0.01),
stringsAsFactors = FALSE)
)
a5 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :---- | :-------------------- | :-- | :---- | :-------------------- |
| G1: | 2,500 | with probability 0.33 | G2: | 2,400 | with probability 0.33 |
| | 2,400 | with probability 0.66 | | 2,400 | with probability 0.66 |
| | 0 | with probability 0.01 | | 2,400 | with probability 0.01 |
deal_is_transparent(a5)
#> [1] TRUE
deal_make_transparent(a5) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :---- | :-------------------- | :-- | :---- | :-------------------- |
| G1: | 2,500 | with probability 0.33 | G2: | 2,400 | with probability 0.33 |
| | 2,400 | with probability 0.66 | | 2,400 | with probability 0.66 |
| | 0 | with probability 0.01 | | 2,400 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a5))
#> [1] TRUE
a6 <- list(
data.frame(
x=c(2500, 0),
p=c(0.33, 0.67),
stringsAsFactors = FALSE),
data.frame(
x=c(2400, 0),
p=c(0.34, 0.66),
stringsAsFactors = FALSE)
)
a6 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :---- | :-------------------- | :-- | :---- | :-------------------- |
| G1: | 2,500 | with probability 0.33 | G2: | 2,400 | with probability 0.34 |
| | 0 | with probability 0.67 | | 0 | with probability 0.66 |
deal_is_transparent(a6)
#> [1] FALSE
deal_make_transparent(a6) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :---- | :-------------------- | :-- | :---- | :-------------------- |
| G1: | 0 | with probability 0.66 | G2: | 0 | with probability 0.66 |
| | 2,500 | with probability 0.33 | | 2,400 | with probability 0.33 |
| | 0 | with probability 0.01 | | 2,400 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a6))
#> [1] TRUE
The following pair of deals constitute Allais Paradox. Second deal is
proportionate copy of the first one.
a7 <- list(
data.frame(
x=c(4000, 0),
p=c(0.8, 0.2),
stringsAsFactors=FALSE),
data.frame(
x=c(3000),
p=c(1),
stringsAsFactors = FALSE)
)
a7 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :---- | :------------------- | :-- | :---- | :----------------- |
| G1: | 4,000 | with probability 0.8 | G2: | 3,000 | with probability 1 |
| | 0 | with probability 0.2 | | | |
deal_is_transparent(a7)
#> [1] FALSE
deal_make_transparent(a7) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :---- | :------------------- | :-- | :---- | :------------------- |
| G1: | 0 | with probability 0.2 | G2: | 3,000 | with probability 0.2 |
| | 4,000 | with probability 0.8 | | 3,000 | with probability 0.8 |
deal_is_transparent(deal_make_transparent(a7))
#> [1] TRUE
a8 <- list(
data.frame(
x=c(4000, 0),
p=c(0.2, 0.8),
stringsAsFactors=FALSE),
data.frame(
x=c(3000, 0),
p=c(0.25, 0.75),
stringsAsFactors = FALSE)
)
a8 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :---- | :------------------- | :-- | :---- | :-------------------- |
| G1: | 4,000 | with probability 0.2 | G2: | 3,000 | with probability 0.25 |
| | 0 | with probability 0.8 | | 0 | with probability 0.75 |
deal_is_transparent(a8)
#> [1] FALSE
deal_make_transparent(a8) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :---- | :-------------------- | :-- | :---- | :-------------------- |
| G1: | 0 | with probability 0.75 | G2: | 0 | with probability 0.75 |
| | 4,000 | with probability 0.20 | | 3,000 | with probability 0.20 |
| | 0 | with probability 0.05 | | 3,000 | with probability 0.05 |
deal_is_transparent(deal_make_transparent(a8))
#> [1] TRUE
The following pair of deals exemplify Ellsberg Paradox.
a9r <- list(
data.frame(
x=c(8, 0),
p=c(0.1, 0.9),
stringsAsFactors=FALSE),
data.frame(
x=c(20, 0),
p=c(0.05, 0.95),
stringsAsFactors = FALSE)
)
a9r %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :- | :------------------- | :-- | :- | :-------------------- |
| G1: | 8 | with probability 0.1 | G2: | 20 | with probability 0.05 |
| | 0 | with probability 0.9 | | 0 | with probability 0.95 |
deal_is_transparent(a9r)
#> [1] FALSE
deal_make_transparent(a9r) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :- | :-------------------- | :-- | :- | :-------------------- |
| G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 |
| | 8 | with probability 0.05 | | 20 | with probability 0.05 |
| | 8 | with probability 0.05 | | 0 | with probability 0.05 |
deal_is_transparent(deal_make_transparent(a9r))
#> [1] TRUE
a9b <- list(
data.frame(
x=c(8, 0),
p=c(0.6, 0.4),
stringsAsFactors=FALSE),
data.frame(
x=c(20, 0),
p=c(0.3, 0.7),
stringsAsFactors = FALSE)
)
a9b %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :- | :------------------- | :-- | :- | :------------------- |
| G1: | 8 | with probability 0.6 | G2: | 20 | with probability 0.3 |
| | 0 | with probability 0.4 | | 0 | with probability 0.7 |
deal_is_transparent(a9b)
#> [1] FALSE
deal_make_transparent(a9b) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | |
| :-- | :- | :------------------- | :-- | :- | :------------------- |
| G1: | 0 | with probability 0.4 | G2: | 0 | with probability 0.4 |
| | 8 | with probability 0.3 | | 20 | with probability 0.3 |
| | 8 | with probability 0.3 | | 0 | with probability 0.3 |
deal_is_transparent(deal_make_transparent(a9b))
#> [1] TRUE
References:
Leland, J. W., Schneider, M., & Wilcox, N. T. (2019). Minimal Frames and
Transparent Frames for Risk, Time, and Uncertainty. Management Science.
Stochastic dominance:
http://nejchladnik.com/blog/2015/11/14/the-concept-of-stochastic-dominance/
dmi3kno/deals documentation built on Dec. 11, 2019, 12:07 p.m.
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deals
The purpose of deals is to faclitiate operations with and presentation
of decisions under uncertainty.
Installation
You can install the released version of deals from Github with:
remotes::install_github("dmi3kno/deals")
Example
This is a basic example which shows you how to solve a common problem:
library(deals)
library(magrittr)
## basic example code
Transparent deals
Leland, Schneider, & Wilcox (2019) introduced definition of “transparent
frames” for decisions under uncertainty (hereafter, “deals”). In this
package a deal is a list of two dataframes, each with two columns p
(probability of a given outcome) and x (the outcome itself). Decision
maker is offered a choice between two uncertain prospects and can choose
one of them.
# Allais paradox
a1 <- list(
data.frame(
x=c(5e5),
p=c(1),
stringsAsFactors = FALSE),
data.frame(
x=c(2.5e6, 5e5, 0),
p=c(0.1, 0.89, 0.01),
stringsAsFactors = FALSE)
)
a1 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :------ | :----------------- | :-- | :-------- | :-------------------- | | G1: | 500,000 | with probability 1 | G2: | 2,500,000 | with probability 0.10 | | | | | | 500,000 | with probability 0.89 | | | | | | 0 | with probability 0.01 |
deal_is_transparent(a1)
#> [1] FALSE
deal_make_transparent(a1) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :------ | :-------------------- | :-- | :-------- | :-------------------- | | G1: | 500,000 | with probability 0.89 | G2: | 500,000 | with probability 0.89 | | | 500,000 | with probability 0.10 | | 2,500,000 | with probability 0.10 | | | 500,000 | with probability 0.01 | | 0 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a1))
#> [1] TRUE
a2 <- list(
data.frame(
x=c(5e5,0),
p=c(0.11,0.89),
stringsAsFactors = FALSE),
data.frame(
x=c(2.5e6,0),
p=c(0.10,0.90),
stringsAsFactors = FALSE)
)
a2 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :------ | :-------------------- | :-- | :-------- | :------------------- | | G1: | 500,000 | with probability 0.11 | G2: | 2,500,000 | with probability 0.1 | | | 0 | with probability 0.89 | | 0 | with probability 0.9 |
deal_is_transparent(a2)
#> [1] FALSE
deal_make_transparent(a2) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :------ | :-------------------- | :-- | :-------- | :-------------------- | | G1: | 0 | with probability 0.89 | G2: | 0 | with probability 0.89 | | | 500,000 | with probability 0.10 | | 2,500,000 | with probability 0.10 | | | 500,000 | with probability 0.01 | | 0 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a2))
#> [1] TRUE
a3 <- list(
data.frame(
x=c(0, 45, 30, -15, -15),
p=c(0.9, 0.06, 0.01, 0.01, 0.02),
stringsAsFactors = FALSE),
data.frame(
x=c(0, 45, 45, -10, -15),
p=c(0.9, 0.06, 0.01, 0.01, 0.02),
stringsAsFactors = FALSE)
)
a3 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :--- | :-------------------- | :-- | :--- | :-------------------- | | G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 | | | 45 | with probability 0.06 | | 45 | with probability 0.06 | | | 30 | with probability 0.01 | | 45 | with probability 0.01 | | | -15 | with probability 0.01 | | -10 | with probability 0.01 | | | -15 | with probability 0.02 | | -15 | with probability 0.02 |
# this one is transparent
deal_is_transparent(a3)
#> [1] TRUE
deal_make_transparent(a3) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :--- | :-------------------- | :-- | :--- | :-------------------- | | G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 | | | 45 | with probability 0.06 | | 45 | with probability 0.06 | | | 30 | with probability 0.01 | | 45 | with probability 0.01 | | | -15 | with probability 0.01 | | -10 | with probability 0.01 | | | -15 | with probability 0.02 | | -15 | with probability 0.02 |
deal_is_transparent(deal_make_transparent(a3))
#> [1] TRUE
a4 <- list(
data.frame(
x=c(0, 45, 30, -15),
p=c(0.9, 0.06, 0.01, 0.03),
stringsAsFactors = FALSE),
data.frame(
x=c(0, 45, -10, -15),
p=c(0.9, 0.07, 0.01, 0.02),
stringsAsFactors = FALSE)
)
a4 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :--- | :-------------------- | :-- | :--- | :-------------------- | | G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 | | | 45 | with probability 0.06 | | 45 | with probability 0.07 | | | 30 | with probability 0.01 | | -10 | with probability 0.01 | | | -15 | with probability 0.03 | | -15 | with probability 0.02 |
deal_is_transparent(a4)
#> [1] FALSE
deal_make_transparent(a4) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :--- | :-------------------- | :-- | :--- | :-------------------- | | G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 | | | 45 | with probability 0.06 | | 45 | with probability 0.06 | | | -15 | with probability 0.02 | | -15 | with probability 0.02 | | | 30 | with probability 0.01 | | 45 | with probability 0.01 | | | 0 | with probability 0.00 | | 0 | with probability 0.00 | | | -15 | with probability 0.01 | | -10 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a4))
#> [1] TRUE
a5 <- list(
data.frame(
x=c(2500, 2400, 0),
p=c(0.33, 0.66, 0.01),
stringsAsFactors = FALSE),
data.frame(
x=c(2400, 2400, 2400),
p=c(0.33, 0.66, 0.01),
stringsAsFactors = FALSE)
)
a5 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :---- | :-------------------- | :-- | :---- | :-------------------- | | G1: | 2,500 | with probability 0.33 | G2: | 2,400 | with probability 0.33 | | | 2,400 | with probability 0.66 | | 2,400 | with probability 0.66 | | | 0 | with probability 0.01 | | 2,400 | with probability 0.01 |
deal_is_transparent(a5)
#> [1] TRUE
deal_make_transparent(a5) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :---- | :-------------------- | :-- | :---- | :-------------------- | | G1: | 2,500 | with probability 0.33 | G2: | 2,400 | with probability 0.33 | | | 2,400 | with probability 0.66 | | 2,400 | with probability 0.66 | | | 0 | with probability 0.01 | | 2,400 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a5))
#> [1] TRUE
a6 <- list(
data.frame(
x=c(2500, 0),
p=c(0.33, 0.67),
stringsAsFactors = FALSE),
data.frame(
x=c(2400, 0),
p=c(0.34, 0.66),
stringsAsFactors = FALSE)
)
a6 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :---- | :-------------------- | :-- | :---- | :-------------------- | | G1: | 2,500 | with probability 0.33 | G2: | 2,400 | with probability 0.34 | | | 0 | with probability 0.67 | | 0 | with probability 0.66 |
deal_is_transparent(a6)
#> [1] FALSE
deal_make_transparent(a6) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :---- | :-------------------- | :-- | :---- | :-------------------- | | G1: | 0 | with probability 0.66 | G2: | 0 | with probability 0.66 | | | 2,500 | with probability 0.33 | | 2,400 | with probability 0.33 | | | 0 | with probability 0.01 | | 2,400 | with probability 0.01 |
deal_is_transparent(deal_make_transparent(a6))
#> [1] TRUE
The following pair of deals constitute Allais Paradox. Second deal is proportionate copy of the first one.
a7 <- list(
data.frame(
x=c(4000, 0),
p=c(0.8, 0.2),
stringsAsFactors=FALSE),
data.frame(
x=c(3000),
p=c(1),
stringsAsFactors = FALSE)
)
a7 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :---- | :------------------- | :-- | :---- | :----------------- | | G1: | 4,000 | with probability 0.8 | G2: | 3,000 | with probability 1 | | | 0 | with probability 0.2 | | | |
deal_is_transparent(a7)
#> [1] FALSE
deal_make_transparent(a7) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :---- | :------------------- | :-- | :---- | :------------------- | | G1: | 0 | with probability 0.2 | G2: | 3,000 | with probability 0.2 | | | 4,000 | with probability 0.8 | | 3,000 | with probability 0.8 |
deal_is_transparent(deal_make_transparent(a7))
#> [1] TRUE
a8 <- list(
data.frame(
x=c(4000, 0),
p=c(0.2, 0.8),
stringsAsFactors=FALSE),
data.frame(
x=c(3000, 0),
p=c(0.25, 0.75),
stringsAsFactors = FALSE)
)
a8 %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :---- | :------------------- | :-- | :---- | :-------------------- | | G1: | 4,000 | with probability 0.2 | G2: | 3,000 | with probability 0.25 | | | 0 | with probability 0.8 | | 0 | with probability 0.75 |
deal_is_transparent(a8)
#> [1] FALSE
deal_make_transparent(a8) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :---- | :-------------------- | :-- | :---- | :-------------------- | | G1: | 0 | with probability 0.75 | G2: | 0 | with probability 0.75 | | | 4,000 | with probability 0.20 | | 3,000 | with probability 0.20 | | | 0 | with probability 0.05 | | 3,000 | with probability 0.05 |
deal_is_transparent(deal_make_transparent(a8))
#> [1] TRUE
The following pair of deals exemplify Ellsberg Paradox.
a9r <- list(
data.frame(
x=c(8, 0),
p=c(0.1, 0.9),
stringsAsFactors=FALSE),
data.frame(
x=c(20, 0),
p=c(0.05, 0.95),
stringsAsFactors = FALSE)
)
a9r %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :- | :------------------- | :-- | :- | :-------------------- | | G1: | 8 | with probability 0.1 | G2: | 20 | with probability 0.05 | | | 0 | with probability 0.9 | | 0 | with probability 0.95 |
deal_is_transparent(a9r)
#> [1] FALSE
deal_make_transparent(a9r) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :- | :-------------------- | :-- | :- | :-------------------- | | G1: | 0 | with probability 0.90 | G2: | 0 | with probability 0.90 | | | 8 | with probability 0.05 | | 20 | with probability 0.05 | | | 8 | with probability 0.05 | | 0 | with probability 0.05 |
deal_is_transparent(deal_make_transparent(a9r))
#> [1] TRUE
a9b <- list(
data.frame(
x=c(8, 0),
p=c(0.6, 0.4),
stringsAsFactors=FALSE),
data.frame(
x=c(20, 0),
p=c(0.3, 0.7),
stringsAsFactors = FALSE)
)
a9b %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :- | :------------------- | :-- | :- | :------------------- | | G1: | 8 | with probability 0.6 | G2: | 20 | with probability 0.3 | | | 0 | with probability 0.4 | | 0 | with probability 0.7 |
deal_is_transparent(a9b)
#> [1] FALSE
deal_make_transparent(a9b) %>%
deal_to_textdf() %>%
knitr::kable(col.names = NULL)
| | | | | | | | :-- | :- | :------------------- | :-- | :- | :------------------- | | G1: | 0 | with probability 0.4 | G2: | 0 | with probability 0.4 | | | 8 | with probability 0.3 | | 20 | with probability 0.3 | | | 8 | with probability 0.3 | | 0 | with probability 0.3 |
deal_is_transparent(deal_make_transparent(a9b))
#> [1] TRUE
References:
Leland, J. W., Schneider, M., & Wilcox, N. T. (2019). Minimal Frames and Transparent Frames for Risk, Time, and Uncertainty. Management Science.
Stochastic dominance: http://nejchladnik.com/blog/2015/11/14/the-concept-of-stochastic-dominance/
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