What is a Zero-Sum Game?

A zero-sum game is like squeezing a balloon…

When you squeeze a balloon, you change its shape. But, unless you pop the balloon, you haven’t changed the amount of air that’s inside. Putting pressure on one part of the balloon merely moves the same air around. Likewise, a zero-sum game doesn’t add anything to the financial system. It just rearranges what was already there.

A “game” is any situation with players, strategies, and rewards. Any interaction between people, whether it’s a sport, a negotiation, an interview, or a charitable event, can be viewed as a game. The study of game theory examines how people interact with one another in these games. It explores the strategies that people use to improve their circumstances — Especially when other people are trying to improve their circumstances, too.

Games are zero-sum if winners and losers cancel each other out. For instance, for one team to win a basketball game, the other side must lose. Or, if you take a dollar away from one person and give it to someone else, that is zero-sum. Zero-sum games rearrange a finite amount of something. It’s like sharing a pie. Because there's a limited amount, taking a bigger piece forces someone else to have a smaller share.

Game theory has probably existed informally for a long time. The first known written discussion on the topic seems to be a letter between Charles and James Waldegrave in 1713. The details are shaky, but the letter solves a two-person card game.

Antoine Augustin Cournot is also sometimes given credit as a founder of zero-sum game theory. In his 1838 work titled Researches into the Mathematical Principles of the Theory of Wealth, Cournot presents a solution to a pricing problem between competing firms. What he describes is now known as a Nash equilibrium.

Other notable works advanced the scientific community’s knowledge of strategy. But it was John Von Neumann and Oskar Morgenstern who wrote the book on the subject. In 1944, the two wrote Theory of Games and Economic Behavior, which drew heavily on Von Neumann’s 1928 paper titled On the Theory of Games and Strategy.

The 1950s saw a flood of interest in game theory. Its application grew across many fields, from nuclear physics to political science. John Nash was among the notable thought leaders of the time and developed a proof that expanded the applicability of game theory solutions. The Nash equilibrium remains a relevant and important finding.

In economic theory, most games aren't zero-sum. It ‘s tempting to think that the exchange of goods is zero-sum. After all, one person gets the other person’s money. But, contrary to popular belief, economics isn't the study of money. It’s the study of allocating scarce resources. When a trade occurs, it improves that allocation. That's because people have different tastes, preferences, and budgets. So, the price a person pays doesn’t fully reflect the value they receive.

For instance, imagine you agree to give your neighbor a dozen eggs for a gallon of milk. For that trade to happen, you must prefer the gallon of milk to the dozen eggs. That means you end up happier after the deal. At the same time, your neighbor must prefer a dozen eggs to a gallon of milk. So, they're also happier after the trade. Since both of you are better off, it’s not a zero-sum game. All voluntary trade, whether it’s done through bartering or with money, does more than rearrange possessions. It always creates intangible gains from trade. As a result, pure zero-sum games are uncommon in economics.

Options (contracts that provide the right, but not the obligation to buy or sell something at a predetermined price) and futures (contracts for the advanced purchase or sale of something) are sometimes considered zero-sum games, or at least as close as you can get. True zero-sum games don’t provide any net benefits to the participants. One wins, and the other loses. Options and futures contracts kind of work this way. When the contract ends, one person is happy with the result, and the other isn't. For example, if the price goes up substantially, one investor will make a profit. That profit comes from somewhere making it a zero-sum game.

This is different from buying or selling the stock directly. If a stock’s price goes up after you sell it, that’s not a loss to you. Just as your car getting hit by a falling tree after you sell it has no impact on you. But, options and futures are more like bets on the direction a stock will move in the future. When the contract closes, one person was right and the other was wrong. With an option, the premium (cost of buying the contract) moves from the buyer to the seller regardless of the outcome. If the buyer executes a call option, the seller ends up giving up their security for less than the current market price. At the settlement of a futures contract, money transfers out of one account and into another more directly. From the perspective of looking at all investors and traders in aggregate, these are zero-sum games.

But, there may be some benefits that aren’t captured by looking solely at the money changing hands. For instance, an investor that buys or sells a future might be hedging against volatility. With a predetermined price locked in, the investor removes some risk from their portfolio. That risk reduction is a benefit to someone that is risk averse, regardless of whether the price moves in a favorable direction or not. From this perspective, options and futures might not be zero-sum.

Political decisions are often considered zero-sum games. In some cases, that is more accurate than in others. Elections are zero-sum by definition. There’s one winner and one loser, just like in sports or board games. A vote cast for one party is a vote against the other.

Government policies can be zero-sum, positive-sum, or negative-sum. The key is whether the policy is effective or not. For instance, taxing one person and giving that money to another person might be considered zero-sum. If such a redistribution of wealth doesn’t improve a social problem, that is more likely to be the case. But, if that program corrects a market failure, it could help one person more than it hurts the others.

This utilitarian approach (making sure that the total social good outweighs the overall harmful impacts of a decision) to governance is arguably a positive-sum game. Ineffective political choices can be negative-sum games. For instance, well-intentioned trade barriers, like tariffs, can reduce the benefits of international trade for both partners.

Two-person zero-sum games are situations in which two people are competing over a finite goal or resource. What one person gets, the other person loses — aka non-cooperative games. A one-on-one basketball game is a two-player zero-sum game, as is most gambling between two people. Negotiations are often two-party zero-sum games, where the parties are each trying to get as much of the potential profits as possible. Although the deal in its entirety is positive-sum, the distribution of the gains is not.

For example, imagine that a person owns some land with high-quality timber. A logging company might approach the owner and offer to cut and sell the trees. Assume the sales price for all of the lumber would be $1M. If they agree to a deal, there’s $1M of value that wouldn’t exist without an agreement. That means the contract itself is positive-sum. But, the negotiations around how much of that $1M each party gets is a two-party zero-sum game. Every dollar the logging company gets is a dollar the owner doesn’t.

The opposite of a zero-sum game is a non-zero-sum game. With a zero-sum game, adding up all the costs and benefits equals zero. They’re win-lose situations. But that’s not always the case. There are non-zero-sum games, where everyone wins, everyone loses, or the total costs and benefits are just not equal.

In many situations, the benefits are greater than the costs. That would be a positive-sum game. International trade is an example of a positive-sum game. By focusing resources on doing what each country does best, then trading with each other, the residents of both nations end up getting better prices. The exporting country sells its product for more than it would get domestically, and the importing country receives a lower price than it would pay internally. That’s a win-win. Although there are negative impacts involved, the benefits usually outweigh the costs.

In other situations, everyone is worse off than if the scenario never existed. For instance, a labor union going on strike is a lose-lose proposition in the short-run. The workers lose their paychecks, and the business loses its production. That’s a negative-sum game — Unless there are substantial long-term gains. The same is true with predatory pricing strategies, in which a large company reduces its prices to bankrupt the competition.

*Options trading entails significant risk and is not appropriate for all investors. Certain complex options strategies carry additional risk. To learn more about the risks associated with options trading, please review the options disclosure document entitled Characteristics and Risks of Standardized Options, available here or through https://www.theocc.com. Investors should consider their investment objectives and risks carefully before trading options. Supporting documentation for any claims, if applicable, will be furnished upon request.