Suppose you're part of a game with a large, unknown number of players, and each player is given 100 coins of equal value to start. Here's how the game works: each round, all players anonymously put an undisclosed amount of coins -- up to 20 -- into the central pot. Once each player has done this, all players are returned the average amount of coins put into the pot (total coins divided by number of players) plus 25% of that average. The game continues for 5 rounds.
How many coins would you put into the pot each round, and why?
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If the game continues for 5 rounds, then one should assume that noone puts in anything - in a long game (infinite / indeterminate end) it can be possible to establish cooperation. However, as soon as there is a distinct, finite end to that game then backwards induction implies a payment into the pot of zero.
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Edited by A Good Troll: 1/14/2013 7:56:51 PMPersonally, I'd put in nothing and take the guaranteed return with no risk to my own coins. Worst case scenario is I get nothing if everyone does what I do. I have no worry of a loss. Thanks for the free moneyz Neuron.
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Edited by FoMan123: 1/14/2013 7:56:03 PMI love game theory. Much like the prisoner's dilemma, this works out best for everybody if everyone trusts everyone else to cooperate. And thus this works out in an ideal world if everyone puts the maximum amount of coins in the pot each round. In that case, the group profits at the maximum level. The selfish player, of course, will put the minimum amount of coins in and will gain the most individual profit. If enough players are selfish, the players who put the most coins into the pot will suffer a loss, not a profit, while the selfish players will enjoy a profit at others' expense. If ALL the players are selfish, nobody will profit at all. Therefore, like most theoretical games, my answer would depend on who else I know is playing. With a large, unknown number of (apparently anonymous) players, most rational, logical people -- including me, personally -- would put in the minimum amount of coins to reduce the personal risk and maximize the potential profit. This particular hypothetical effectively demonstrates why taxes are mandatory :-D
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Edited by Malfar: 1/14/2013 5:14:00 PM20, because I'd want the highest return. I have a question, lets say you put in 20 coins, and after the first round you get back 5, how many people could be playing? Now lets say you get back 100 coins after the first round, how many people could be playing?
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I was expecting Saw references