Even in a room full of game theorists, will the winner be at one. There are a few considerations. One is that one person who slips up either through a misunderstanding or spite will throw off the average. Another consideration is that if you win with zero or one, you will have to split any prize pool with many other players.
Yes, but if you guess higher than 0 (in, as you say, spite) then you only hurt yourself, since everyone else ties for the win. The choice of 0 in this game is a Nash equilibrium - no rational agent will guess otherwise, at least if it assumes all other agents are also rational.
This is true, but I was specifically addressing the case where a "spiteful" agent attempts to guess high and throw off the average, and just pointing out that this would actually hurt no one but the spiteful agent himself.
