Algowikiadmin: Recovering wiki

2014-09-11T18:23:24Z

Recovering wiki

Algowikiadmin: Recovering wiki

2014-09-11T18:13:51Z

Recovering wiki

New page

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} -> (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:

<pre>
{1,2} -> (0, 600)
{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:

<pre>
{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)
</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 ...

@@ Line 1: / Line 1: @@
 Let's start at the end and look at the process after we get to just two pirates (labeled by seniority in increasing order):
-&lt;pre&gt;
+<pre>
-{1, 2}     -&gt; (0, 600)
+{1, 2}     -> (0, 600)
-&lt;/pre&gt;
+</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:
-&lt;pre&gt;
+<pre>
-{1,2}      -&gt; (0, 600)
+{1,2}      -> (0, 600)
-{1,2,3}    -&gt; (1,   0, 599)
+{1,2,3}    -> (1,   0, 599)
-&lt;/pre&gt;
+</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:
-&lt;pre&gt;
+<pre>
-{1,2}         -&gt; (0, 600)
+{1,2}         -> (0, 600)
-{1,2,3}       -&gt; (1,   0, 599)
+{1,2,3}       -> (1,   0, 599)
-{1,2,3,4}     -&gt; (0,   1,   0, 599)
+{1,2,3,4}     -> (0,   1,   0, 599)
-{1,2,3,4,5}   -&gt; (1,   0,   1,   0, 598)
+{1,2,3,4,5}   -> (1,   0,   1,   0, 598)
-(1,2,3,4,5,6} -&gt; (0,   1,   0,   1,   0, 598)
+(1,2,3,4,5,6} -> (0,   1,   0,   1,   0, 598)
-&lt;/pre&gt;
+</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 ...

TADM2E 2.51 - Revision history

Algowikiadmin: Recovering wiki

Algowikiadmin: Recovering wiki