Game Theory of Communism and Capitalism

Game Theory of Communism and Capitalism
by Dean Michael Gores

In this article I model and examine two most popular economic systems with game theory: Communism and Capitalism. My models will be pure Communism and pure Capitalism, both are not possible due to cheaters in the real world, but they can be implemented to a close approximation.

The US is not pure capitalism, although it may have been the closest to pure capitalism between 1800 and 1900. Uncaught thieves, fraudulent activity, murder, and other natural right infringing activities make a capitalist economic system non-pure. Today and since the early 1900's the US has been more of a mixed capitalist/communist economy: people still keep a portion of the products of their labor, but significant portions of their labor are redistributed to others. I presume the cause of the US's shift towards communism is an increasing portion of the population that prefers to live at the expense of others.

Russia and China once attempted to implement communism. Russia was closest to pure Communism between 1922 and 1989, and China between 1949 and 1979. Similar problems such as thieves, fraudulent activity, and murder also made these societies’ economic systems non-pure, among larger issues such as non-equal redistribution of wealth (more given to those in power) and cheaters who would keep and hide their wealth creation instead of handing it over to the government. After mass starvation in Russia and China the populations have moved towards more capitalist economic systems.

Moving beyond my historical introduction to “pure” Communism and Capitalism, I will now present mathematical analysis of these systems using game theory. Game theory is a tool used in decision making, particularly when other people's decisions influence the rewards of your choices. In game theory, the goal is to maximize your gains and minimize your losses. You expect others will make choices that are best for themselves. Below are the choices an individual has in each pure economic system, and the results of the individual's choices.

Imagine a Simple Situation where people can choose to between working and relaxing. Each day, a person consumes 1 day's worth of values such as food, shelter, and water that enables them to live. When a person works a day, they create enough life enabling values for a person to survive 4 days (values such as acquiring/creating food/shelter/water/etc). When a person works a day, their extra effort for working that day makes them hungrier and puts more wear on their belongings, costing them an extra 1/2 day of values. When a person relaxes through a day, they do not create any values, but they still consume 1 day's worth of values.

I hope that you agree that this Simple Situation is not far from the situation we currently live in. There are variations in how much value an individual makes from day to day, and some individuals can be extremely productive on some days (such as an inventor’s or a CEO’s life altering insight). And some people consume more values each day to survive, and various degrees of extra effort and wear from work. But from the equations I derive in the analysis below, these variations are not extremely important. For simplicity’s sake and improved understanding, let me continue with the simple model where every individual is equally productive when they work and equal in the other respects.

Simple Situation Summary:
Work: loose 1 day of value for living, create 4 days of value, but loose 1/2 day of value from effort and wear
Relax: loose 1 day of value for living, create 0 days of value

Now let me propose two ways to distribute the values created through work: The "Communist" way: All values created are divided evenly amongst all people. The "Capitalist" way: Each person who works keeps all the values that they themselves create. With this information, I can create tables to compare the net gains resulting from a person’s choice of whether to work or relax, taking into account other’s decisions on working or relaxing. I created four tables for Communism (Tables 1-4) and four tables for Capitalism (Tables 5-8) to discover what happens in different population sizes.

Each table is separated into the choice of person ‘A’ to either Work or Relax. In each row I start with the number of other people that decide to work in the population. Then I calculated the total value created by the entire population.

Table 1-4. Results of the "Capitalist" way from an individual's (named 'A') perspective, with various numbers of people in the economy:

Table 5-8. Results of the "Communist" way from an individual's (named 'A') perspective, with various numbers of people in the economy:

With examination of the tables above, a few conclusions can be formed about the Communist system:
1. In the smallest group case of two people, there is 1.5 days of value more gained by working v relaxing (2.5 - 1.0) and (0.5 - (-1.0)) = 1.5.
2. In small groups, it can be expected that a person will choose to work rather than relax, because no matter how many other people are working, it is always more rewarding for an individual to work.
3. In large groups, it can be expected that a person will choose to relax rather than work, because no matter how many other people are working, it is always more rewarding for an individual to relax.
4. For the studious, you will find that the benefit of working over relaxing is = (value created in a day's work) / (# of people) - (the extra cost of working). Example: for 2 people, 4/2 - 0.5 = 1.5. For 5 people: 4/5 - 0.5 = 0.3. For 10 people: 4/10 - 0.5 = -0.1. For 100 people: 4/100 - 0.5 = -0.46. Limit as population approaches infinity: 4/INF - 0.5 ~= 0 - 0.5 = -0.5.
5. For the studious, you will find that the group size where the net reward is the same whether a person works or relaxes is = (the value created in a day's work) / (the extra cost of working over relaxing). Example: In this model: 4 / 0.5 = 8 people.

With examination of the tables above, a few conclusions can be formed about the Capitalist system:
1. No matter how many people are in the population, and no matter whether others choose to work, an individual's rewards for working and relaxing do not change.
2. There is always 3.5 days of value more gained by working vs relaxing (2.5 - (-1.0)) = 3.5.
3. For the studious, you will find that the benefit of working over relaxing is = (value created in a day's work) - (the extra cost of working). Example: 4 - 0.5 = 3.5.

Comparing the two systems:
1. The motivation for working in Capitalism always exceeds the motivation for working in Communism. In our example, from 2 to 4 days of value more is gained from working in Capitalism vs working in Communism. In the group size of two: 3.5 - 1.5 = 2. In the infinite group size: 3.5 - (-0.5) = 4.
2. In Communism in the "large group" case, it’s more beneficial to relax than to work, which leads to a massive shortage of values. Capitalism does not have this issue, since its rewards are independent of group size.
3. For the studious, note the difference in equations for calculating the benefit of working over relaxing in the two systems:
Communism: (value created in a day's work) / (# of people) - (the extra cost of working)
Capitalism: (value created in a day's work) - (the extra cost of working)
The equations are very similar, except in Communism you only receive a fraction of the value you create. This is the source of why in larger groups it becomes more rewarding to relax rather than work.

Observations related to a society becoming more Communist (by "revolution" or popular vote):

During the revolution where all currently existing values are "evenly" redistributed, the poor and those in power instantly gain a lot of values, which is a short term motivation for their desire to have such a revolution and make the population become more Communist. Those who recently had values are devastated. This is a different situation than the simulation above. Above is the aftermath, the long term trend. For those who care about the short term, and wish to minimize their effort, Communism is the choice. Examples: Lenin, Stalin, Mao, Wesley Mouch, Mr. Thompson, Dr. Robert Stadler.

For those who care about the long term, and wish to maximize their rewards, Capitalism is the choice. The only thing that prevents a society from becoming more Communist is that the producers disallow the wealth redistributors from taking their wealth. Remove their reward, remove their motivation to perform such an action. To maximize the rewards of your work over the long term, you must disallow others from gaining from attempting to take your wealth. Examples: The USA Founding Fathers, John Galt, Francisco d'Anconia, Ragnar Danneskjöld.

Home work: What are the game theory tables and what are some interesting equations in a 50/50 mixed economy? What are the equations when we make the fraction of socialism a variable?

Discuss this Article (51 messages)