Voluntary contributions

Messaggioda Fioravante Patrone » 07/07/2007, 17:30

You are going to play the following game.

You are one among a group of six players. The players (you included) don't know each other. Moreover, you are put in a cubiculum with a screen in front. Communication will take place only via the screen and keyboard.
At the end of the game, everyone will leave independently, without seeing each other. So, not only you did not know each other before the game, but the same will be true also after you have played.

Everyone receives 20 euro.
He can decide how much of these euro to put in a common pot. The money that he will not put in the pot will remain his.
The decision will be communicated via keyboard, without knowing the choices made by the other five participants.
All of the money collected in the pot will be multiplied by three and then divided evenly among the six participants.

How much do you put in the common pot? (The answers allowed must be an integer number ranging from 0 to 20, extremes included)


Please DO NOT ANSWER before Sunday at noon. Leave room to potential participants to ask questions, further information.
Please answer using the "Spoiler" to allow participants to give their answer without knowing your choice.
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Messaggioda wedge » 07/07/2007, 19:47

dear professor Patrone, how does the keyboard fit in the game? can everyone write everything on it?
what's the meaning of communicating the decision via keyboard if everyone has no access to others' choices?
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Messaggioda Fioravante Patrone » 07/07/2007, 19:59

wedge ha scritto:dear professor Patrone

:lol:


wedge ha scritto:how does the keyboard fit in the game? can everyone write everything on it?
what's the meaning of communicating the decision via keyboard if everyone has no access to others' choices?


the main point is that each one of the six players will express his choice privately and in an anonymous way
the secrecy of his choice is guaranteed by the fact that it will be typed by him on a keyboard (so that he cannot be identified by the other players)
every player will have a reserved space (like cabins for elections) with his keyboard
the choices of every one will be recorded by a computer, so that the (small!) computations needed to find how much has earned each of the players
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Messaggioda wedge » 07/07/2007, 20:15

thanks, everything is clear to me now (except the solution)

is heavy-combinatorics required?
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Messaggioda Fioravante Patrone » 07/07/2007, 22:56

you "must" choose an integer number between 0 and 20

that you base your choice on:
- heavy combinatorics
- gut feelings
- bright intuitions and powerful theorems
- how many birds you saw today
is up to you!
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Messaggioda fields » 08/07/2007, 11:30

Do we have to justify our answer? Maybe it's better we do not explain our choice to avoid influence on the other players...
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Messaggioda wedge » 08/07/2007, 11:41

Here I am!

Testo nascosto, fai click qui per vederlo
It's a matter of generosity and trust. If I leave x in the pot, I lose x/2 but everyone else gains x/2. The difference between my money before and my money after the game is in fact:

D = -x/2 + 5/2 y

where y is the average of others' contributions.
If I were extremely egoistic I would think "I'll put 0 in the pot, so I'll be sure of not losing anything"
But obviously if everyone puts 0, there's no possibility of profit.
So, do I trust other people to give me something? I suppose that everyone has an attitude similar to mine, so x is similar to y. Maybe that's not perfectly true, so I suppose that y may range from x-2 to x+2.
My aim is to gain at least 5. So, in the worst case where y=x-2,

D = -x/2 + 5/2 x-2 = 5

It means x=5. I'll put 5 in the pot. If each other player puts more than 3 in the pot, I'll gain more than 5. If I got wrong with everything and everyone deals with egoism, I'll lose only 2.5. In order not to lose money I just need each of them to put 1. I think a more negative conclusion is so remote! This strategy ensure me a gain of about 5 with a risk of 2.5


Fioravante, please leave a comment (spoiler-way). I'm curious!

edit: errore del mio English! non ho cambiato la risposta ;)
Ultima modifica di wedge il 09/07/2007, 20:57, modificato 1 volta in totale.
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Messaggioda Fioravante Patrone » 08/07/2007, 11:56

fields ha scritto:Do we have to justify our answer? Maybe it's better we do not explain our choice to avoid influence on the other players...

no, you don't have to justify you answer
but I strongly suggest that you do, so that the thread will be more interesting

please leave your answer and justifications (if any) hidden in the spoiler
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Messaggioda Fioravante Patrone » 08/07/2007, 11:57

wedge ha scritto:Fioravante, please leave a comment (spoiler-way). I'm curious!


I will comment extensively on the answers received. But later...
Enjoy the remaining part of this holiday!
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Messaggioda Kroldar » 08/07/2007, 14:22

Testo nascosto, fai click qui per vederlo
Answer: $0$
In my opinion, the problem is to find a probability distribution for the other players. But I don't anything about the other players so I can't guess the probability distribution I would need. In this case, the maxmin strategy could be a good choice. I won't be wondered if also the other players think the same thing... in fact the combination of strategies $(0,0,0,0,0,0)$ is a Nash equilibrium for the game.


1 - wedge
2 - Kroldar
....
We need 4 other players :wink:
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