Why do trades occur?

[mathemagician54]

maybe this is a silly question, but why do trades occur?

Assume that we have intelligent players and players are willing to buy/sell iff they believe a stock to be under/over valued, ie for example someones not willing to sell just because he needs some $ right away, even if he believes holding the stock to be +EV.

Now if I believe a stock to be undervalued, i will buy it from someone who believes it to be overvalued. But when I learn that this person believes the stock to be overvalued, that will change my valuation of the stock since there's something he may know that I don't. Similarly his valuation of the stock should increase. If we keep increasing the level of thought, i.e he knows that I know that he believes the stock to be overvalued, yet I still buy it, that will continue to change his valuation even more until it seems like we're in some sort of equilibrium where none of us believe that it is profitable to buy or sell.

clearly this doesn't happen in the real world though. What's wrong with this argument?