Indeed the article is poor. His beauty contest results are more plausibly explained by anchoring bias (start at 2 thirds of 100). EMH is about price dynamics so a single "run" of the beauty contest says nothing about it. I am willing to bet a significant amount that after a couple of iterations, the bids would go to zero.

I simply dont see The "paradox" the author thinks they have discovered. There is reams of empirical evidence that active fund management is GENERALLY a losing proposition for savers. Both parties to a trade can end up losers because trading costs are never zero. If you want to go quickly broke, just keep blindly buying and selling over and over. Even if you beat the spread, the fees will swallow your money.

No but that has been done in the experimental economics literature: http://web.stanford.edu/~niederle/GuessingGames.pdf (see slide 11)

The answer is: the mean gradually approaches zero.