It can be defined by the net present value of the future dividends of the stock. Alternately, it can be determined by the per-share liquidation value of the company's assets (after creditors are paid).

So if the stock does not pay dividends, and never will, and the corporation's assets equal its liabilities, and always will, then the appropriate value of the stock is, in fact, zero? (Well, there are voting rights, but still...)

No, the value also includes the NPV of future net earnings, even if they are not currently being paid as dividends. When you value a business for the purpose of selling it, revenue, assets and intangibles like brand awareness are all things you look at.

Also if a company's assets = its liabilities then it has not been profitable or its losing money (or its a very new business). Obviously failing businesses are not worth anything and stock prices reflect that; but a business that is earning a net profit has a value regardless of if dividends are paid. If dividends are not paid they are re-invested in the business, which isn't really different from you getting the dividend and investing it in that or some other stock except that you are giving the company's management credit for making wise investments (bonuses are an expense and are sub-tracted from net income and so are not relevant here).

(Myself, I sort of suspect that, if a stock doesn't pay dividends, it's mostly worthless. To quote some guy with a blog:

If you put your Mickey Mantle rookie card on your desk, and a share of your favorite non-dividend paying stock next to it, and let it sit there for 20 years. After 20 years you would still just have two pieces of paper sitting on your desk.) Maybe it would help to think of a sole proprieter running a small retail business who starts with perhaps $500k in personal equity. He pays himself a relatively meager salary and invests all other net income back into the business to increase inventory, advertise, move to a better location or open another branch etc. After running this business for forty years its expanded successfully and worth $8MM dollars, even though it hasn't paid a single dividend. Did he waste the last forty years of his life? Do you think he'll be able to extract that earned value?

From there you should be able to see that a privately held corporation (only owned by family) could work exactly the same, and from that its not a leap at all to see how a publically held company can increase in value without ever actually extracting the value from it.

3) There is some other explanation, which I have not yet thought of.

Maybe the sales of the game on the other platform will be more profitable than the PS3 sales they miss out on? The margin for games is much higher than for consoles and you definitely can broaden your market by including 360 owners who do not wish to shell out $400 just to play that game. Is it conceivably possible that Sony knows as much or more about the gaming industry as you do?

I'm not sure if you'll find this interesting, but I quit smoking using something like the method you are describing. Basically I labeled the craving for nicotine as an entity apart from myself - I named it "the beast". So instead of thinking "I want a smoke" I'd think: "the beast is hungry." This didn't work all by itself (I had a lot of practice quitting) but it was the last of 5-6 attempts to quit and its stuck for nearly ten years now.