Difference between revisions of "TADM2E 2.51"
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Let's start at the end and look at the process after we get to just two pirates (labeled by seniority in increasing order): | Let's start at the end and look at the process after we get to just two pirates (labeled by seniority in increasing order): | ||
| − | + | <pre> | |
| − | {1, 2} - | + | {1, 2} -> (0, 600) |
| − | + | </pre> | |
since pirate 2 just takes all the money for himself and has 50% of the vote. Now, we step up to the case of three pirates where pirate 3 makes use of this fact to bribe pirate 1 to give him his vote and avoid the two pirate state where he gets nothing: | since pirate 2 just takes all the money for himself and has 50% of the vote. Now, we step up to the case of three pirates where pirate 3 makes use of this fact to bribe pirate 1 to give him his vote and avoid the two pirate state where he gets nothing: | ||
| − | + | <pre> | |
| − | {1,2} - | + | {1,2} -> (0, 600) |
| − | {1,2,3} - | + | {1,2,3} -> (1, 0, 599) |
| − | + | </pre> | |
Now, we just continue this process with each pirate bribing the pirates who would get 0 in previous case until we get to the six pirate case: | Now, we just continue this process with each pirate bribing the pirates who would get 0 in previous case until we get to the six pirate case: | ||
| − | + | <pre> | |
| − | {1,2} - | + | {1,2} -> (0, 600) |
| − | {1,2,3} - | + | {1,2,3} -> (1, 0, 599) |
| − | {1,2,3,4} - | + | {1,2,3,4} -> (0, 1, 0, 599) |
| − | {1,2,3,4,5} - | + | {1,2,3,4,5} -> (1, 0, 1, 0, 598) |
| − | (1,2,3,4,5,6} - | + | (1,2,3,4,5,6} -> (0, 1, 0, 1, 0, 598) |
| − | + | </pre> | |
Since each stage is stable then pirates 2, 4, and 6 have incentive to vote yes since the next stage is stable and would result in them receiving less ... | Since each stage is stable then pirates 2, 4, and 6 have incentive to vote yes since the next stage is stable and would result in them receiving less ... | ||
Latest revision as of 18:23, 11 September 2014
Let's start at the end and look at the process after we get to just two pirates (labeled by seniority in increasing order):
{1, 2} -> (0, 600)
since pirate 2 just takes all the money for himself and has 50% of the vote. Now, we step up to the case of three pirates where pirate 3 makes use of this fact to bribe pirate 1 to give him his vote and avoid the two pirate state where he gets nothing:
{1,2} -> (0, 600)
{1,2,3} -> (1, 0, 599)
Now, we just continue this process with each pirate bribing the pirates who would get 0 in previous case until we get to the six pirate case:
{1,2} -> (0, 600)
{1,2,3} -> (1, 0, 599)
{1,2,3,4} -> (0, 1, 0, 599)
{1,2,3,4,5} -> (1, 0, 1, 0, 598)
(1,2,3,4,5,6} -> (0, 1, 0, 1, 0, 598)
Since each stage is stable then pirates 2, 4, and 6 have incentive to vote yes since the next stage is stable and would result in them receiving less ...
