Zero-Sum Games

A zero-sum game is a situation that arises in game theory, where there are clear winners and losers and where the winners gains exactly offset the losers losses. In other words, there is no net benefit to all participants when playing these games. Please note that the word game is used in the context of game theory and applies to any situation where there are multiple participants involved in an activity.

The situation can arise where a game is zero-sum in nature, but non-zero-sum in practice. Take forex trading for example, this will apply to futures and options as well. These activities are all zero-sum in that one traders win is offset by another traders loss, but they do not sum to zero in practice. In fact after commissions are subtracted from both traders, the game is actually negative non-zero. In other words, two traders buying and selling contracts from each other, both will lose in the long run as they pay more and more commission.

The concept can however be moved beyond an accounting perspective and actually change the game into a positive non-zero game. Take for example a professional futures trader and an importer who enter into a contract. The importer is willing to pay the commission to ensure that the price today is guaranteed at a set time in the future. At the same time, the trader is looking to lock in the difference between the price today, and the delivery price for the importer. Lets take a look at an example to better explain this concept.

Example

An importer wants to purchase 100 ounces of gold at the current price of $600 per ounce in 6 months time. However, he does not want to take on any additional risk and is not willing to pay more than $600 + Commissions. So he takes out a futures contract that allows him to purchase 100 ounces of gold at $600 per ounce, 6 months from today. At the same time, a speculator decides that he believes that the price of gold will decrease over the next 6 months and he takes the other end of the importers contract on a speculative basis. They both pay commission for the service and thus the game starts off in negative non-zero-sum territory.

6 months later, the price of gold is $550 per ounce. The importer would have preferred to pay $550, but he is happy to know that he doesn't have to pay more than $600. The trader has made a profit of $50 per ounce for a total of $5000 and the brokerage has earned their fees.

As you can see in the above example, sometimes zero-sum games result in all parties being happy. In other words a win-win situation. This changes the dynamic of the game and actually makes it a non-zero-sum game.

In contrast to futures, forex and options, stock trading is a non-zero sum game and that's why stock trading is the most popular form of trading in society. On average people gain from the capital investments that they make in companies whether your interest be in a stock directly or a mutual fund, ETF, pension plan or one of many other routes into the stock market. The reason for this is twofold. Firstly society benefits by having increased capital in industries that need capital (after all people only allocate money where they believe it is needed). Companies get access to this initial capital by releasing an IPO. At the same time, investors benefit in that they are not competing against each. In other words, one investor doesn't lose money as a result of another investors gains assuming that foregone profits are not losses.

Example

Bob buys ABC stock for $20 and sells it for $25 to Jim. Jim then sells the stock to Tom for $30.

Although Bob could have made an extra $5 per share if he had waited and sold directly to Tom, he would not, and should not, consider that extra $5 a loss. Instead one should notice in the scenario, that both Bob and Jim benefited, and it wasn't at the expense of Tom. If the stock decreases to $20, resulting in a $10 loss for Tom, it is still not Zero-Sum because the loss didn't occur because of the corresponding $10 profit, but rather bad timing in the market by Tom. The loss was only his fault and Bob and Jim never benefited from Tom's loss.

Ultimately society wants to increase the amount of positive non-zero-sumness as it results in a net gain for society as a whole. This concept can be applied to economics and trading as well.