Predator-prey dynamical systems are idealized descriptions of behavior in the animal kingdom, an unforgiving domain from which humans imagine their superior evolutionary development and civilization afford them some protection.
This simulation of a repeated game illustrates a mathematical notion of economic class dominance within a population assumed to be partitioned into classes. One class dominates another if, at each repetition of the game, the payoff to the class is an asymmetric zero-sum transfer of utility from the other class, proportional to the population of the other class.
The idea to define economic class dominance as a population-dependent income transfer from one class to another was suggested by a New York Times article of December 25, 2009, entitled "At Tiny Rates, Saving Money Costs Investors." The Times reported that "...risk-averse investors are effectively financing a second bailout of financial institutions, many of which have also raised fees and interest rates on credit cards." William H. Gross of Pimco was quoted. "...a significant part of the government’s plan to repair the financial system and the economy is to pay savers nothing and allow damaged financial institutions to earn a nice, guaranteed spread," he said.
In this simulation, a population is partitioned into two classes called the Bourgeois, representing the banks, and the Proletariat, representing the depositors, who earn a fixed working wage. The Bourgeois dominate the Proletariat in the above sense. Income in this simulation is identified with population: one person = one unit (one dollar). The payoff to the Proletariat at each repetition of the game is a population-independent constant fixed for the entire simulation.
Each play of the repeated game proceeds as follows. Two members of the total population are selected uniformly at random. If both are Proletariat, the Proletariat population (income) is increased by a constant amount. If one is Proletariat and the other is Bourgeois, a fixed fraction of the Proletariat becomes Bourgeois (some of the Proles are eaten by the Bourgeois). Finally, if both are Bourgeois, one of them dies and the other becomes Proletariat. That's life in the big city.
Load the source code prole.R into an R session with source('prole.R').
Create a PROLE object (called sim for definiteness) with sim <- new("PROLE", 1000, 2, 30, 40, 0.031), for example.
Plot the simulation with plot(sim). This will produce ggplot2 output, such as the following.
The method density(sim) will produce a density plot of the Bourgeois and Proletariat population distributions for the simulation. The color-coded dashed lines indicate distribution
means. 
(c) 2010-2012, Florian Lengyel florian.lengyel@gmail.com The text is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA-3.0) license. The code is licensed under the GNU General Public License, version 2.