Don't need to know every color's happiness, given the bias towards positive happiness. Keep in mind the happiness could be really random. Another reason is seeing other groupo is requiring that color a lot, which means we can benifit a lot from trading with that color without know the happiness of that color. The initial number of each color should also be considerated.
As long as know one color is of 1.0 happiness, you don't care whether there is
other color of 1.0 happiness since focus on one good color gives optimal result.
When it is hard to pick between two colors, hold on both. Later on, when one color accumulates more and more, the decision will be more apparent given the quadratic happiness curve.
Luck also counts. How early can you discover the best color to hold?
Given the quadratic dependence on the number, the difference between happiness contributes less.
Possible for the players to cooperate to follow a certain communication strategy such that all the players have a better knowledge of others' preference and everyone achieves global optimization? Is this kind of cooperation stable? How to assure your own benifit during a cooperation? Keep in mind that the communication is really limited. This may ruin the cooperation even everyone is trying to be nice. (Think about prisoner lemma)
Think in a bigger scale. The tournament score is sum over many games. Second rank every game may give you the champion after all games.
You are only one among many people giving offers. Does it worth to scrifice a little to make sure your offer has higher possibility to be picked?
Multiple games among the same group of players such that people have time to learn each other.
Lier could be identified by inconsistent behavior. Punish the lier hard and hide yourself harder. (You guys are really sophisticated...)
What if there are just too many colors that each color will not have number large enough to feed one single player? Even if there are less colors than players, there will still be some pathetic players have to eat more than one color.
Keep record of former trades, see what others like and dislike. Could be a count matrix.
Deliverable:
A little sophisticated player.
Offer and desire for the same color means something.
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