Re: Twenty Bank Robbers -- solution (?)

["Robert A. Rosenberg" <hal9001@panix.com>]

At 17:32 -0500 7/25/96, John Deters wrote:


>At 01:13 PM 7/25/96 -0500, Igor Chudov wrote:
>>Igor Chudov wrote:
>>>
>>> Here's a puzzle for our game theorists.
>>
>>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.
>
>The first cypherpunk should propose a 10-way split:  #s 11-20.  It's the
>best offer #s 10-18 will be assured of getting without having to kill
>anyone.  Once any one dies, I think the results will always boil down to #19
>getting 100% of the money (when #s 1-18 are dead, #19 proposes that #19 gets
>100% of the money and his vote is 50%, so he "wins".  #20 kills him out of
>spite and takes it all anyway, though.  No honor amongst thieves.)

As I noted in a separate message, I think that if the killing starts it
will not necessarily go as far as you propose. Since, when it is #17's
change, all he needs is one extra vote, he can offer to split with #20
(who, as you note, will get nothing from #19 - so it is in his interest to
accept any offer from #17 that is for at least 50% [anything less he
should/could reject since #18 will/should offer him at least 50% to prevent
#18 getting killed]).

Also, I question WHO #1 should offer the split to. All he wants is 9 extra
votes so it does not need to be #11-20. I'd think that #1-10 (if #1 wants
part of the money) or #2-11 (if he does not but wants to hedge his bet by
allowing for one "No" vote from that group) would be better since by voting
"YES", each gets to not need to worry about coming up with a split or
risking death (11-20 do not have this type of immediate threat hanging over
their heads so they are more likely to vote "NO" and hope for a better deal
[as the first ones start dropping dead, there are less votes needed so the
"I'll Bribe you with part of the Split" offers are going to be worth more
to those who are included]).