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)

Modified the problem from this post to also include debt. If someone doesn't have the funds to pay during the turn, they have to borrow money from the person they should be giving it to, and pay back with interest. I'll attach the resulting simulation in the next comment.

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.