I firmly hold that all financial contracts are zero-sum games. Recently, however, I have heard many arguments premised on the idea that the stock market is positive sum because economic growth creates wealth, which is reflected in universally rising stock prices.
But in this scenario, you purchase $1 of stock on Day 1. On Day 100, thanks to robust economic growth, you sell your stock for $100. Are you wealthier? Yes. Has the amount of wealth in the world increased? No. All that's happened is that someone else has given you $100. Wealth has been transferred but not invented.
In a more general sense: when you buy a stock, you give cash to someone in return for the stock certificate. Later, when you sell the stock, you hand the certificate to someone else in return for their cash. It does not matter whether the amount of cash at the end is more than that at the beginning or less - no cash has been created by this process.
This is not surprising, as it is well known that stock trades in the "secondary market" - which is to say, the market not directly related to the issuing corporation. But even IPO's do not create wealth - they merely gather cash from many investors who are (suddenly) willing to hand it over to a single company. True, the company may use that cash to generate new wealth - but that is now outside the realm of the stock certificate, which remains a zero sum game in the secondary market.
There is one possible exception. Dividends provide a mechanism by which money is transferred directly from the wealth-generating company to the holder of an otherwise zero-sum game. In other words, an entitiy outside the zero-sum realm is giving money to someone within it - shouldn't that necessitate dividend-paying stocks as positive sum games? I believe it does not. When dividends are paid, the stock drops in value by the amount of the dividend, ensuring that the holder does not get paid twice for the same dividend. (Incidentally, the same logic led Modigliani and Miller to conclude that dividends are irrelevant in a frictionless world, because any investor can create his own dividends by selling shares of stock). Since the sum of an investor's cash and the value of a stock he holds is identical immediately before and after the dividend is paid, I conclude that dividends do not create a positive-sum environment.
Thus, stocks do uphold the premise of a zero-sum game: no wealth is created, it is merely transferred. To the extent that wealth is created and injected into the system via dividends, the value of the stock drops by an equal amount, so the net value remains unchanged. The search for positive-sum finance continues...