This reminds me of the way prices are set in the stock market. Nobody really knows how much a share is worth; that is to some degree unknowable. But people will try to guess how much the share is worth, and then buy or sell it if the prevailing price is noticeably more or less than their estimate, and it's widely believed that the prices set by that process accurate reflect the value of the business.
But after a while it can turn into a game of buying and selling where nobody really cares about the underlying business anymore, they're just trying to guess the averages that will come out of the marketplace process... and then that's the situation where you dispense with the jar of jelly beans.
You game has an interesting wrinkle to it if we start thinking about players trying to manipulate the game. If I guess a huge large or small number, much larger than I expect the other players to be guessing, that gives me the opportunity to manipulate the average.
If I'm playing only for myself, there's no advantage to doing that. Say there are a hundred players guessing in the range of 0 to 1000, and I come in and guess a googol. Then I've pretty much set how the game will go - the average will be about 1/100th of a googol, far away from all the other players, and it's obvious I can put the average wherever I want - but I don't win because those other players are much closer. I have to pull my own guess far away from the average in order to be sure of controlling the average. I can't rig the game so that I win, but I can rig it so that the player other than me who guesses the greatest (or least) number wins.
So what happens if I have a confederate, I guess a googol, my confederate guesses 1/1000th of a googol, and everyone else guesses in the range 0 to 1000? Then my confederate wins.
It seems like the game is stable as long as people don't collude - we'll all tend to "cooperate" by guessing numbers near where we think the average of cooperating guesses will be, and that will tend to be close to zero because that's the only really distinguished real number.
But if people attempting to collude in pairs is a common enough thing that we expect it to happen at least once per game, then it seems like it will turn into a contest of who can think of the biggest numbers, because a pair wins if they scale their strategy to be bigger than anyone else's.
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But after a while it can turn into a game of buying and selling where nobody really cares about the underlying business anymore, they're just trying to guess the averages that will come out of the marketplace process... and then that's the situation where you dispense with the jar of jelly beans.
You game has an interesting wrinkle to it if we start thinking about players trying to manipulate the game. If I guess a huge large or small number, much larger than I expect the other players to be guessing, that gives me the opportunity to manipulate the average.
If I'm playing only for myself, there's no advantage to doing that. Say there are a hundred players guessing in the range of 0 to 1000, and I come in and guess a googol. Then I've pretty much set how the game will go - the average will be about 1/100th of a googol, far away from all the other players, and it's obvious I can put the average wherever I want - but I don't win because those other players are much closer. I have to pull my own guess far away from the average in order to be sure of controlling the average. I can't rig the game so that I win, but I can rig it so that the player other than me who guesses the greatest (or least) number wins.
So what happens if I have a confederate, I guess a googol, my confederate guesses 1/1000th of a googol, and everyone else guesses in the range 0 to 1000? Then my confederate wins.
It seems like the game is stable as long as people don't collude - we'll all tend to "cooperate" by guessing numbers near where we think the average of cooperating guesses will be, and that will tend to be close to zero because that's the only really distinguished real number.
But if people attempting to collude in pairs is a common enough thing that we expect it to happen at least once per game, then it seems like it will turn into a contest of who can think of the biggest numbers, because a pair wins if they scale their strategy to be bigger than anyone else's.