-----BEGIN PGP SIGNED MESSAGE----- Assuming "perfect" intelligence on the part of the robbers (i.e. they will follow deterministic behavior and do the "right" thing), then here's what must happen IMO (1 being the first guy and 20 being the last): 1 must propose that 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 all split the money evenly. All of these will vote for it, assuming they're all perfectly smart and deduce the inevitable outcome. I arrived at this working backward from the case where two robbers are left. If 2 are left (19 & 20), 19 gets all the money. So 20 will vote for whatever 18 says, which MUST include 20 in the deal. Since 19 knows this, 19 will vote for whatever 17 says, which must include 19 in the deal, and so forth. Eventually you arrive at the conclusion that 1,3,5...,19 must all agree to split the money at the beginning. On Thu, 25 Jul 1996, Igor Chudov wrote:

Igor Chudov wrote:

...

Here's a puzzle for our game theorists.

Twenty cypherpunks robbed a bank. They took 20 million bucks. Here's how they plan to split the money: they stay in line, and the first guy suggests how to split the money. Then they vote on his suggestion. If 50% or more vote for his proposal, his suggestion is adopted.

Otherwise they kill the first robber and now it is the turn of guy #2 to make another splitting proposal. Same voting rules apply.

The question is, what will be the outcome? How will they split the money, how many robbers will be dead, and so on?

I forgot to say what the GOALS are. The goals of every individual cypherpunk are (in from highest to lowest priority):

1. Stay alive 2. Get as much money as possible 3. Keep as many cypherpunks alive as possible, all other things being equal.

- Igor.

- -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Jeremey Barrett Senior Software Engineer jeremey@forequest.com The ForeQuest Company http://www.forequest.com/ "less is more." -- Mies van de Rohe. Ken Thompson has an automobile which he helped design. Unlike most automobiles, it has neither speedometer, nor gas gage, nor any of the numerous idiot lights which plague the modern driver. Rather, if the driver makes any mistake, a giant "?" lights up in the center of the dashboard. "The experienced driver", he says, "will usually know what's wrong." -- 'fortune` output -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQCVAwUBMfgENS/fy+vkqMxNAQEauAP+Ns7g50LTtdRmLg8/ffoveH6x6o/ml6a8 ELGw6/gA0oRq81gVDA/q48uUDOK3+RirV+HcAnB3/QobocxgqftOvcpwk6ewCLOB bh0f2u8OpcXd/ArrC+Upi4l87Eo1IONDudsluaEVYCBX6cTmyrK3kRskjue/3Xr6 I0UIlz6UxFE= =lvhl -----END PGP SIGNATURE-----

First, the line is established before the proposals begin. So the proposer is not determined by lot, everyone knows who will be #1, #2, etc. Second, I think the proposer gets to vote. The wording is a bit ambiguous, but it just says that "they" vote, and I think "they" pretty clearly refers to the whole group. Now here is the solution for two people: #1 (first in line) proposes that he gets it all. #1 votes yes, #2 votes no. The proposal passes. Here it is for three people: #1 (first in line) proposes that he gets it all. #1 votes yes, #2 probably votes no (since he will get it all if the proposal fails, by the above) and #3 (end of line) reasons like this: if the proposal fails, he (#3) will get nothing because #2 will get it all. Therefore voting yes or no makes no difference to whether #3 stays alive (his first priority) or how much money he makes (his second priority). But it does make a difference in terms of keeping as many people alive as possible (his third priority). So he votes yes because of this third reason. Therefore the proposal passes and the first person in line gets it all in this case. Of course, #1 could have offered some money to #3 and gotten his vote, but that would violate the terms of the problem: #1 wants to make as much money as possible. And since he can get #3's vote even while offering nothing to him, that is what he will do. Hal

At 6:59 AM -0700 7/26/96, Hal wrote:

First, the line is established before the proposals begin. So the proposer is not determined by lot, everyone knows who will be #1, #2, etc. Second, I think the proposer gets to vote. The wording is a bit ambiguous, but it just says that "they" vote, and I think "they" pretty clearly refers to the whole group.

Now here is the solution for two people:

#1 (first in line) proposes that he gets it all. #1 votes yes, #2 votes no. The proposal passes.

Here it is for three people:

#1 (first in line) proposes that he gets it all. #1 votes yes, #2 probably votes no (since he will get it all if the proposal fails, by the above) and #3 (end of line) reasons like this: if the proposal fails, he (#3) will get nothing because #2 will get it all. Therefore voting yes or no makes no difference to whether #3 stays alive (his first priority) or how much money he makes (his second priority). But it does make a difference in terms of keeping as many people alive as possible (his third priority). So he votes yes because of this third reason. Therefore the proposal passes and the first person in line gets it all in this case.

Of course, #1 could have offered some money to #3 and gotten his vote, but that would violate the terms of the problem: #1 wants to make as much money as possible. And since he can get #3's vote even while offering nothing to him, that is what he will do.

But Hal, these are Cypherpunks, which means some of them are smart and some are uh, er, um, not so smart. I would not want to be first in line. David