Business Investor Model

Overview

This report presents analyses and visualizations of the Business Investor Model described in Railsback & Grimm (2019). The model simulates interactions between businesses and investors to demonstrate fundamental concepts in agent-based modeling (ABM).

Model 10.4.2

Setting the Environment

library(brandr)
library(dplyr)
library(ggplot2)
library(here)
library(janitor)
library(patchwork)
library(readr)
library(stats)

Figure 10.1.1

data <-
  here::here(
    "data",
    "business-investor-model-10-4-2-figure-10-1-1-table.csv"
  ) |>
  readr::read_csv(
    skip = 6,
    col_types = readr::cols(.default = "c")
  ) |>
  janitor::clean_names() |>
  dplyr::select(
    run_number,
    sensing_radius,
    mean_wealth_of_investors,
    standard_deviation_wealth_of_investors
  ) |>
  dplyr::mutate(
    dplyr::across(
      .cols = dplyr::everything(),
      .fns = as.numeric
    )
  ) |>
  dplyr::summarize(
    mean = mean(mean_wealth_of_investors, na.rm = TRUE),
    sd = mean(standard_deviation_wealth_of_investors, na.rm = TRUE),
    .by = sensing_radius
  )

data

data |>
  ggplot2::ggplot() +
  ggplot2::geom_point(
    mapping = ggplot2::aes(x = sensing_radius, y = mean),
    size = 3,
    shape = 19,
  ) +
  ggplot2::geom_point(
    mapping = ggplot2::aes(x = sensing_radius, y = sd),
    size = 3,
    shape = 8,
  ) +
  ggplot2::scale_x_continuous(breaks = seq(0, 10, 2)) +
  ggplot2::scale_y_continuous(
    breaks = seq(0, 700000, 100000),
    labels = ~ prettyNum(.x, big.mark = ","),
    limits = c(0, 700000)
  ) +
  ggplot2::labs(
    x = "Sensing radius",
    y = "Mean final investor wealth"
  )
#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).

Figure 10.1.2

data <-
  here::here(
    "data",
    "business-investor-model-10-4-2-figure-10-1-2-table.csv"
  ) |>
  readr::read_csv(
    skip = 6,
    col_types = readr::cols(.default = "c")
  ) |>
  janitor::clean_names() |>
  dplyr::select(
    run_number,
    step,
    sensing_radius,
    mean_wealth_of_investors
  ) |>
  dplyr::mutate(
    dplyr::across(
      .cols = dplyr::everything(),
      .fns = as.numeric
    )
  ) |>
  dplyr::mutate(
    sensing_radius = factor(sensing_radius, ordered = TRUE)
  ) |>

  dplyr::summarize(
    mean = mean(mean_wealth_of_investors, na.rm = TRUE),
    .by = c("step", "sensing_radius")
  )

data

data |>
  ggplot2::ggplot(ggplot2::aes(x = step, y = mean, color = sensing_radius)) +
  ggplot2::geom_line(linewidth = 1) +
  ggplot2::scale_x_continuous(breaks = seq(0, 50, 10)) +
  ggplot2::scale_y_continuous(
    breaks = seq(0, 700000, 100000),
    labels = ~ prettyNum(.x, big.mark = ","),
    limits = c(0, 700000)
  ) +
  ggplot2::labs(
    x = "Year",
    y = "Mean investor wealth",
    color = "Sensing radius"
  ) +
  brandr::scale_color_brand_d()

Model 11.5

Figure 12.1

data <-
  here::here(
    "data",
    "business-investor-model-11-5-figure-12-1-table.csv"
  ) |>
  readr::read_csv(
    skip = 6,
    col_types = readr::cols(.default = "c")
  ) |>
  janitor::clean_names() |>
  dplyr::select(
    run_number,
    decision_time_horizon,
    mean_wealth_of_investors,
    mean_profit_of_turtles_on_patches,
    mean_risk_of_failing_of_turtles_on_patches,
    total_business_failures
  ) |>
  dplyr::mutate(
    dplyr::across(
      .cols = dplyr::everything(),
      .fns = as.numeric
    )
  ) |>
  dplyr::mutate(
    decision_time_horizon = factor(decision_time_horizon, ordered = TRUE)
  )

data

plot_1 <-
  data |>
  dplyr::summarize(
    mean = mean(mean_wealth_of_investors, na.rm = TRUE),
    sd = stats::sd(mean_wealth_of_investors, na.rm = TRUE),
    .by = decision_time_horizon
  ) |>
  ggplot2::ggplot(
    ggplot2::aes(
      x = decision_time_horizon,
      y = mean,
      ymin = mean - sd,
      ymax = mean + sd
    )
  ) +
  ggplot2::geom_point(shape = 19) +
  ggplot2::geom_errorbar(linewidth = 0.2) +
  ggplot2::scale_x_discrete(breaks = seq(0, 25, 5)) +
  ggplot2::scale_y_continuous(
    breaks = seq(0, 400000, 100000),
    labels = ~ prettyNum(.x, big.mark = ","),
    limits = c(0, 400000)
  ) +
  ggplot2::labs(
    x = "Time horizon (years)",
    y = "Mean final investor wealth"
  )

plot_2 <-
  data |>
  dplyr::summarize(
    mean = mean(total_business_failures, na.rm = TRUE),
    sd = stats::sd(total_business_failures, na.rm = TRUE),
    .by = decision_time_horizon
  ) |>
  ggplot2::ggplot(
    ggplot2::aes(
      x = decision_time_horizon,
      y = mean,
      ymin = mean - sd,
      ymax = mean + sd
    )
  ) +
  ggplot2::geom_point(shape = 19) +
  ggplot2::geom_errorbar(linewidth = 0.2) +
  ggplot2::scale_x_discrete(breaks = seq(0, 25, 5)) +
  ggplot2::scale_y_continuous(limits = c(0, 80)) +
  ggplot2::labs(
    x = "Time horizon (years)",
    y = "Number of failures"
  )

plot_3 <-
  data |>
  dplyr::summarize(
    mean = mean(mean_profit_of_turtles_on_patches, na.rm = TRUE),
    sd = stats::sd(mean_profit_of_turtles_on_patches, na.rm = TRUE),
    .by = decision_time_horizon
  ) |>
  ggplot2::ggplot(
    ggplot2::aes(
      x = decision_time_horizon,
      y = mean,
      ymin = mean - sd,
      ymax = mean + sd
    )
  ) +
  ggplot2::geom_point(shape = 19) +
  ggplot2::geom_errorbar(linewidth = 0.2) +
  ggplot2::scale_x_discrete(breaks = seq(0, 25, 5)) +
  ggplot2::scale_y_continuous(
    breaks = seq(0, 15000, 5000),
    labels = ~ prettyNum(.x, big.mark = ","),
    limits = c(0, 15000)
  ) +
  ggplot2::labs(
    x = "Time horizon (years)",
    y = "Mean annual profit"
  )

plot_4 <-
  data |>
  dplyr::summarize(
    mean = mean(
      mean_risk_of_failing_of_turtles_on_patches,
      na.rm = TRUE
    ),
    sd = stats::sd(
      mean_risk_of_failing_of_turtles_on_patches,
      na.rm = TRUE
    ),
    .by = decision_time_horizon
  ) |>
  ggplot2::ggplot(
    ggplot2::aes(
      x = decision_time_horizon,
      y = mean,
      ymin = mean - sd,
      ymax = mean + sd
    )
  ) +
  ggplot2::geom_point(shape = 19) +
  ggplot2::geom_errorbar(linewidth = 0.2) +
  ggplot2::scale_x_discrete(breaks = seq(0, 25, 5)) +
  ggplot2::scale_y_continuous(
    breaks = seq(0, 0.05, 0.01),
    labels = ~ prettyNum(.x, big.mark = ","),
    limits = c(0, 0.05)
  ) +
  ggplot2::labs(
    x = "Time horizon (years)",
    y = "Mean annual risk"
  )

patchwork::wrap_plots(
  plot_1, plot_2, plot_3, plot_4,
  ncol = 2,
  axes = "collect_x"
)

Figure 12.2

data <-
  here::here(
    "data",
    "business-investor-model-11-5-figure-12-2-table.csv"
  ) |>
  readr::read_csv(
    skip = 6,
    col_types = readr::cols(.default = "c")
  ) |>
  janitor::clean_names() |>
  dplyr::select(
    run_number,
    step,
    decision_time_horizon,
    mean_risk_of_failing_of_turtles_on_patches
  ) |>
  dplyr::mutate(
    dplyr::across(
      .cols = dplyr::everything(),
      .fns = as.numeric
    )
  ) |>
  dplyr::mutate(
    decision_time_horizon = factor(decision_time_horizon, ordered = TRUE)
  ) |>

  dplyr::summarize(
    mean = mean(mean_risk_of_failing_of_turtles_on_patches, na.rm = TRUE),
    .by = c("step", "decision_time_horizon")
  )

data

data |>
  ggplot2::ggplot(
    ggplot2::aes(
      x = step,
      y = mean,
      color = decision_time_horizon
      # linetype = decision_time_horizon
    )
  ) +
  ggplot2::geom_line(linewidth = 1) +
  ggplot2::scale_x_continuous(breaks = seq(0, 50, 10)) +
  ggplot2::scale_y_continuous(limits = c(0, 0.06)) +
  ggplot2::labs(
    x = "Time step (years)",
    y = "Mean annual risk",
    color = "Time horizon (years)"
    # linetype = "Time horizon (years)"
  ) +
  brandr::scale_color_brand_d()

License

This report is licensed under CC0 1.0 Universal, placing it in the public domain. You may freely copy, modify, distribute, and use this work, even for commercial purposes, without permission or attribution.

References

Railsback, S. F., & Grimm, V. (2019). Agent-based and individual-based modeling: A practical introduction (2nd ed.). Princeton University Press.