I wonder what happens differently if you don't have an obvious fixedpoint, but instead the game is something like "guess closest to 1 bigger than the average of everyone's guess" or maybe "guess closest to 1 bigger than the average of everyone's guess, mod 100". The latter kind of doesn't have any clear strategy, since it's symmetric up to adding n to everybody's answer mod 100. But if you played it repeatedly, maybe you'd see the crowd "chase" forward around Z/100 at some rate... and maybe it'd be interesting if time, in the game, were continuous instead of discrete, and it was up to you to actively change your current guess in real-time reaction to other people changing theirs.
I wonder what happens differently if you don't have an obvious fixedpoint, but instead the game is something like "guess closest to 1 bigger than the average of everyone's guess" or maybe "guess closest to 1 bigger than the average of everyone's guess, mod 100". The latter kind of doesn't have any clear strategy, since it's symmetric up to adding n to everybody's answer mod 100. But if you played it repeatedly, maybe you'd see the crowd "chase" forward around Z/100 at some rate... and maybe it'd be interesting if time, in the game, were continuous instead of discrete, and it was up to you to actively change your current guess in real-time reaction to other people changing theirs.
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