Game Theory 1

Game Theory is the next series of posts that I am going to make. Here's a game-theory problem which I believe is very common in this field. This is a classical problem in which rational players play for their own individual benefit without discussing their move with others. All the players in a game make their moves simultaneously and nobody knows any other player's move before making his own move. In such a game there may not be any agreement between the players to work as a team, because they do not trust one another. (Rational and intelligent people must not trust other rational and intelligent people. I will discuss this in another post someday). Parliamentary election is an example of this game, where voters are the players.

Problem:

There are 5 pirates on a boat, conveniently named 1, 2,3,4,5. These 5 pirates have just dug up a long lost treasure of 100 gold pieces. They now need to split the gold amongst themselves, and they agree to do it in the following way:

Pirate 5 will suggest a distribution of the coins. All pirates other than 5 will vote on his proposal. If an absolute majority approves the plan, then they proceed according to the plan. If he fails to pass his proposal by an absolute majority, then pirate 5 would be killed, and it becomes 4's turn to propose a distribution of the coins among the remaining 4 pirates. They continue this way until either a) a plan has been approved, or b) only pirate 1is still alive (in which case he keeps the whole treasure).

Can you tell how the treasure would be distributed? How many equilibrium states are possible here? The following points must be noted:

• Pirates are very smart (rational). They always think ahead.
  
• Above all else, a pirate must look out for his own life. No pirate wants to die.
  
• After life itself, there is nothing a pirate values more than gold.
  
• A pirate doesn't derive any pleasure from killing any of his fellows. Nor does he have any interest in keeping him alive as far as his own payoff is the same. He would take his decision randomly if his payoff is the same.
  
• Exactly 50% votes in favour does not constitute absolute majority.
  

This is an easy game-theory problem. So, I give the solution away over here. But I am still reluctant to give away the solution of the 12-coins problem, as that was a real brain teaser. If you have a solution or are desperate to have it, drop a comment.

Hint <~~~ Just roll the mouse over it