Tuesday, March 24, 2009

Leaders' competition

Leaders have hard times these days: expectations are high and hope is great. This is a little puzzle, with a lesson inside: a cooperative strategy is important.

You have a list of N Leaders, ordered from the most important to the less important. Each Leader comes with a proposal about how to partition the money among different projects proposed by other leaders. Here are the rules of the game:
  1. Leaders make proposals in order of their importance;
  2. The proposal of the leader i are voted by leaders i, i + 1 , .... N;
  3. A proposal is accepted if it gets the majority of the voting leaders
  4. If a proposal is rejected than the Leader i who proposed it is no longer a Leader, and the proposal of Leader i+1 is therefore voted;
Suppose you are the Leader 0 (e.g. the most important one), what is your cooperative strategy for getting the other Leaders voting your proposal? What if you are Leader i-th can you have your own plan approved?

1 comment:

  1. Ive heard this puzzle, with pirates dividing treasure. The captain decides on a division, and the lower ranked pirates vote. If the majority declines, the captain walks the plank!

    I remember the strategy so I won't spoil it by discussion here, but a good hint is to solve it manually for N=1,2,3,4 and see where that goes.