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Definition: Zero-sum games involve situations in which one person's gains are the result of another person's losses. No wealth is created (or destroyed) in these games.
Examples: Examples of zero-sum games include options and futures. If a person makes money on an options or future contract, it means the person who sold it to him lost money. Another example is gambling: either you or the house win.
What about the stock market? The stock market is not a zero-sum game because stocks are not simply investments traded from one party to another. Rather, they're representative of the underlying business. So if the business creates value, the stock will do so for the investor as well.
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