People in a room giving dollars to random others

simulation.R

library(animation)
library(gganimate)
library(ggplot2)
library(ggthemr)
library(magrittr)
library(tweenr)
library(reshape2)

## Configurable parameters
NUM_PEOPLE    = 45
INITIAL_BANK  = 45
INTEREST_RATE = 0.1
ROUNDS        = 1500
RENT          = 1

## Code that uses these parameters to generate animation
give_money <- function(state) {
  payment_schedule <- sample(seq_along(state$wallets), replace = TRUE)
  for (i in seq_along(state$wallets)) {
    available_cash <- state$wallets[i]
    payout         <- RENT
    if (available_cash < payout) {
      # have to borrow
      their_debt <- state$loans[payment_schedule[i], i]
      if (their_debt > 0) {
        # if they owe me - settle that first
        covered_by_loan <- min(their_debt, payout)
        state$loans[payment_schedule[i], i] %<>% { . - covered_by_loan}
        payout %<>% { . - covered_by_loan }
      }
      # if the whole payout is covered - nothing left to do
      if (payout > 0) {
        if (available_cash < payout) {
          # still not enough money!
          # if there's still something left to pay for - borrow
          loan_amount      <- payout - available_cash
          state$wallets[i] <- 0
          state$wallets[payment_schedule[i]]  %<>% { . + available_cash }
          state$loans[i, payment_schedule[i]] %<>% { . + loan_amount }
        } else {
          # finally enough money to pay
          state$wallets[i]                   %<>% { . - payout }
          state$wallets[payment_schedule[i]] %<>% { . + payout }
        }
      }
    } else {
      # have enough money to pay
      state$wallets[i]                   %<>% { . - payout }
      state$wallets[payment_schedule[i]] %<>% { . + payout }
    }
  }
  state
}

pay_back_the_loans <- function(state) {
  for (x in seq_len(NROW(state$loans))) {
    for (y in seq_len(NCOL(state$loans))) {
      # diagonal is always 0
      if (y != x) {
        debt <- state$loans[x, y]
        available_cash <- state$wallets[x]
        if (debt > 0 && available_cash > 0) {
          payout <- min(available_cash, debt)
          state$loans[x, y] %<>% { . - payout }
          state$wallets[x]  %<>% { . - payout }
        }
      }
    }
  }
  state
}

charge_interest <- function(state) {
  state$loans %<>% { state$loans * (1 + INTEREST_RATE) }
  state
}

last_state <- list(
  wallets = rep(INITIAL_BANK, NUM_PEOPLE),
  loans   = matrix(0, NUM_PEOPLE, NUM_PEOPLE)
)

message("Simulation in progress")
simulation <- pbapply::pblapply(seq_len(ROUNDS), function(x) {
  # a little hack so that animation starts from initial state
  if (x > 1) {
    last_state <<- last_state %>%
      charge_interest         %>%
      pay_back_the_loans      %>%
      give_money
  } else { last_state }
})

message("munging data")
wallet_history <- lapply(simulation, `[[`, "wallets") %>%
  lapply(., function(x) {
    setNames(as.data.frame(lapply(x, identity)), paste0("p", seq_along(x)))
  })

wallet_history <- lapply(seq_along(simulation), function(x) {
  lapply(seq_len(NUM_PEOPLE), function(y) {
    debt <- simulation[[x]]$loans %>% { colSums(.) - rowSums(.) }
    data.frame(
      cash   = simulation[[x]]$wallets[y],
      loans  = debt[y]
    )
  }) %>% plyr::rbind.fill(.)
})

plottable <- tween_states(wallet_history, tweenlength = 1, statelength = 1,
  ease = c("exponential-in-out"),
  nframes = 10)

plottable$player <- as.factor(paste0("p", seq_len(NUM_PEOPLE)))
plottable$debt_free <- (plottable$loans + plottable$cash) >= 0

message("Generating charts")
ggthemr("flat")
p <- ggplot(plottable, aes(frame = .frame, x = player, y = cash+loans, fill = debt_free)) +
  geom_bar(stat = "identity", position = "identity") +
  guides(fill = FALSE)

animation::ani.options(interval = 1/30)
gganimate(p, "simulation.mp4", title_frame = F, ani.width = 1280, ani.height = 720)

Can't attach the gif because of the file size, and can't attach an mp4 because of github's limitations. So I'll just post the final screenshot, and I encourage you to try running this gist on your computer to produce an animation yourself.

The situation seems to destabilize fairly fast towards the last 1% of turns, producing an "economic crisis" with someone getting into an unpayable debt pit, and a handful of players becoming "ultra-wealthy", should the debt ever convert to money. Unfortunately, there isn't enough money in the whole game to account for these numbers.