Boltzman Wealth
In villager: A Framework for Designing and Running Agent Based Models

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(villager)
library(leaflet)

Wealth Exchange

In this model, agents are confined to a bounding box where they move randomly. When two agents are within close range of another, they exchange $1. At the end of the simulation, the wealth distribution is shown as a bar plot. This example was inspired by the "Boltzman Wealth Distribution" model example from Project Mesa.

Location

This simulation takes place in Central Park, New York. The bounding box of the simulation area is shown on the map below.

bounds <- data.frame(latitude = numeric(0), longitude = numeric(0));
# Add the top left point
bounds[nrow(bounds) + 1,] = c(40.772457, -73.975962)
# Add the top right point
bounds[nrow(bounds) + 1,] = c(40.772457, -73.974053)
# Add the bottom left point
bounds[nrow(bounds) + 1,] = c(40.771430, -73.975962)
# Add the bottom right point
bounds[nrow(bounds) + 1,] = c(40.771430, -73.974053)

# Plot them
leaflet::leaflet() %>% 
  leaflet::addTiles() %>%  # Add default OpenStreetMap map tiles
  leaflet::addMarkers (data = bounds) # Add agent locations

Extended Agent

In this example, each agent has its own latitude and longitude. The extended agent class for this follows. For more information on extending agents, check the extending-agents vignette.

gps_agent <- R6::R6Class("agent",
  inherit = villager::agent,
  public = list(
    age = NULL,
    alive = NULL,
    children = NULL,
    father_id = NULL,
    first_name = NULL,
    gender = NULL,
    health = NULL,
    identifier = NULL,
    last_name = NULL,
    mother_id = NULL,
    partner = NULL,
    profession = NULL,
    latitude = NULL,
    longitude = NULL,

    initialize = function(identifier = NA,
                          first_name = NA,
                          last_name = NA,
                          age = 0,
                          mother_id = NA,
                          father_id = NA,
                          partner = NA,
                          children = vector(mode = "character"),
                          gender = NA,
                          profession = NA,
                          alive = TRUE,
                          health = 100,
                          latitude = 0,
                          longitude = 0) {
    super$initialize(identifier,
                     first_name,
                     last_name,
                     age,
                     mother_id,
                     father_id,
                     partner,
                     children,
                     gender,
                     profession,
                     alive,
                     health)
      self$latitude <- latitude
      self$longitude <- longitude
    },

    as_table = function() {
      agent_table <- data.frame(
        age = self$age,
        alive = self$alive,
        father_id = self$father_id,
        first_name = self$first_name,
        gender = self$gender,
        health = self$health,
        identifier = self$identifier,
        last_name = self$last_name,
        mother_id = self$mother_id,
        partner = self$partner,
        profession = self$profession,
        latitude = self$latitude,
        longitude = self$longitude
      )
      return(agent_table)
    }
  )
)

Initial Condition

The simulation initial conditions are: - There are 10 agents - Each agent starts with $10 - The agents start in the center of the bounding box

initial_condition <- function(current_state, model_data, agent_mgr, resource_mgr) {
  # Set the bounding box coordinates by specifying a single point and the max distance that the other corners are
  model_data$events <- list(top_left=list(40.772457, -73.975962), bottom_right=list(40.771430, -73.974053))
  # Create the initial agents (10 of them)
  for (i in seq(10)){
    agent_lat <- 40.77197975
    agent_long <- -73.9750075
    agent <- gps_agent$new(identifier=i, latitude=agent_lat, longitude=agent_long)
    agent_mgr$add_agent(agent)
    # Create the associated money resource
    money <- villager::resource$new(agent$identifier, quantity=10)
    resource_mgr$add_resource(money)
  }
}

Model

The model works by first moving an agent by a random amount. This is equivalent to a random walk. During this process, it's checked whether or not the agent will over-step the bounding box. If they are, the sign of movement is changed so that they move in the opposite direction from the boundary-thus avoiding stepping outside.

Next, The agent checks to see if it's within trading distance of any agents other than itself. If it is, $1 is reduced from its resource cache and is added to the neighbor agent.

test_model <- function(current_state, previous_state, model_data, agent_mgr, resource_mgr) {
  # Loop over each agent and move them
  for (agent in agent_mgr$get_living_agents()) {
    # Generate new coordinates
    delta_lat <- runif(1, -0.00006, 0.00006)
    latitude <- agent$latitude + delta_lat
    delta_long <- runif(1, -0.00006, 0.00006)
    longitude <- agent$longitude + delta_long

    # See if the agent runs out of bounds on the North and West sides
    if (longitude < model_data$events$top_left[[2]] ) {
      # The agent is too far West
      longitude <- agent$longitude - delta_long
    }
    if (latitude > model_data$events$top_left[[1]]) {
      # The agent is too far North
      latitude <- agent$latitude - delta_lat
    }
    # See if the agent runs out of bounds on the South and East sides
    if (longitude > model_data$events$bottom_right[[2]]) {
      # The agent is too far East
      longitude <- agent$longitude - abs(delta_long)
    }
    if (latitude < model_data$events$bottom_right[[1]] ) {
      # The agent is too far South
      latitude <- agent$latitude - delta_lat
    }

    agent$latitude <- latitude
    agent$longitude <- longitude
    # Avoid trading with itseld
    for (neighbor_agent in agent_mgr$get_living_agents()) {
      if (neighbor_agent$identifier == agent$identifier) {
        next
      }
    # Check to see if the neighbor is within this agent's trading region
    lat_range = abs(neighbor_agent$latitude - agent$latitude)
    long_range = abs(neighbor_agent$longitude - agent$longitude)
    if (lat_range < 0.000001 || long_range < 0.000001 ) {
      # Remove $1 from the agent that's currently moving
      money <- resource_mgr$get_resource(agent$identifier)
      # Skip the transfer if the agent doesn't have enough money
      if (money$quantity <= 0) {
        next
      }
      money$quantity <- money$quantity - 1
      # Give it to the neighbor
      money <- resource_mgr$get_resource(neighbor_agent$identifier)
      money$quantity <- money$quantity + 1
    }
  }
  }
}

Running

Create and run a simulation of 10,000 steps.

los_angeles <- village$new("Central_Park", initial_condition, test_model, gps_agent)
simulator <- simulation$new(10000, list(los_angeles))
simulator$run_model()

Results

# Load in data
agent_data <- readr::read_csv("./results/Central_Park/resources.csv")
# Filter the results down to just the last day
data<-agent_data[agent_data$step == 10000, ]
barplot(data$quantity, names.arg=data$name, main="Wealth Distribution", xlab="Agent", ylab="$")