The stock market isn't a zero sum game (or a negative sum game for that matter). If you think it is, you are over simplifying. At the very least you need to account for traders' differing time spans on their trades.

I'm not really game theory expert, but negative sum game is when the total gain is less than total losses, isn't it?

That's exactly what happening - the only source of money are participants, and part of the money goes to brokers.

Say a day trader buys a stock for $9/share and then sells it to me at $10/share a week later. I then put the stock into my investment portfolio and hold on to it for forty years and sell it at $100/share. You could make a simplistic argument that the day trader "lost" the game because he missed out on the appreciation to $100/share but you are neglecting the different investing timespans. The day trader doesn't have a job if he is holding on to stocks for 40 years. He was happy to buy and sell quickly for a small profit. I'm happy because I held on to an appreciating asset. Bankers are happy because they made a few dollars in commissions. No one losses here.

> No one losses here.

But you two are not the whole market. Someone sold a stock to a day trader and someone bought it from you. There are no other money in a stock market except those people bring (minus commission) so how everybody can win?

By being on the positive side, with statistically guaranteed advantage.

(HFT, stat arb, volatility arb, smart automated market making etc.)