What is a zero sum game?
In Economics and Game Theory, a Zero Sum Game is a situation where losses incurred by a contestant in a financial dealing result in a subsequent increase in the gains of the other opposing contestant, such that the net amount after due consideration to conventional positives and negatives turn out to be zero. Contrary to common misbelief, it does not refer to a no profit-no loss scenario for a trader or dealer where the entity manages to conduct business without incurring a loss or registering a profit.
A Zero Sum Game is an explicit contest between opposing parties vying for a prize where a win or gain by one is necessitated by an equal defeat or loss for the opponent. Here, by definition, the piece of business or trade considered for the contest is constant or fixed where no unknown variables are defined or accepted whether before, after or in-game, rendering the whole process a simple matter of calculation and determination with no probable uncertainties involved.
Is the stock market a zero sum game?
Investors’ collective performance in the stock market relative to an index is a zero sum game. Since the value of an index includes all gains and losses, it is by definition, zero sum.
In the context of outperformance (known as “Alpha”) the stock market is a zero sum game because the value of underperformance is equal to the value of outperformance.
The entire stock market system should not be thought of a zero sum game because it does not meet the criteria to be a game with contestants. Only an individual’s performance relative to the stock market index is a game.
What is a non zero sum Game?
A non zero sum game is a situation where there is a net benefit or net loss to the system based on out the outcome of the game.
An example of what should not be considered a non zero sum game is a contest between a trade ship and a pirate ship, although it may look like one at first glance. Here, a victory for the pirates would mean gain of wealth, resources, and men (probably as prisoners), whereas a win for the trade ship would only mean a defeat of the challenge by the pirates. Here, the prize and losses being different for both the contesting parties do not qualify it as an example of a non zero sum game.
Another example of a non zero sum game could be in financial markets, where competing firms collaborate to expand the overall size of their market. Creating an industry-wide organization would increase confidence in the industry and result in more profit for all competitors.
Non zero sum games don’t have to create a net positive result, it could also be negative as well. In the pirate example above, there is a case where the pirates win and it’s a net negative for the whole system.
Origin and Importance
A two-player Zero Sum Game is a perfect competition. Here, not only the resources in the contest are important, but the attitudes, assumptions, and assertions are also parts of the total game. A detailed analysis of a Zero Sum Game would look beyond the result and also how the game was played. This would throw up important observations that could have applications in studying the behavior of consumers, businesses, managers, executives, workers, unions, banks, investors and markets. Such varied implications make Zero Sum Game a viable concept to be developed and studied systematically.
The concept of Zero Sum Game takes root in an archaic idea whereby a win could only be attained through orchestrating the defeat of the opponent. The idea is probably born out of an incorrect understanding of economics and finance where the contested entity was considered fixed and unchangeable and hence, a profit could only be booked by ensuring the loss of competition, resulting in all competitions being understood as Zero Sum Games.
However, modern understanding of economics broadens the scope, explaining that all competitions are not zero sum games as it is possible for all involved contestants to register a win. For example, according to the classical (Ricardian) theory of trade, all parties involved in trade benefit from it. (Trade was often modeled as a zero sum game in the past).