Game theory is a fascinating subject that has applications in various fields, including economics, political science, psychology, and biology. One of the most popular examples of game theory is the Prisoner’s Dilemma. However, another interesting example of game theory is the Pirate Game.
The Pirate Game is a simple but captivating game that involves pirates and their treasure. The game begins with five pirates who have found a treasure of 100 gold coins.
The pirates must decide how to divide the treasure among themselves. However, there are some rules they must follow.
Firstly, the pirates will vote on how to divide the treasure. If more than half of the pirates agree on a plan, then that plan will be implemented. If not, then all the pirates will be killed, and the treasure will remain untouched.
Secondly, the pirates will vote in order of seniority (i.e., from oldest to youngest). Therefore, Pirate 5 will vote first and Pirate 1 last.
Lastly, each pirate wants to maximize their share of the treasure but also wants to stay alive.
So let’s see how this plays out with an example.
Pirate 5 suggests that he should get 100 gold coins because he is the oldest pirate and deserves it. He thinks he can convince Pirate 4 to vote for him by offering him 1 gold coin. Pirates 1-3 would not receive any gold coins under this plan.
Pirate 4 realizes that if he votes for Pirate 5’s plan, he would get one gold coin now but nothing in future rounds since Pirates 1-3 would vote against him in future rounds. He decides to suggest a new plan instead.
Pirate 4 suggests that he gets 99 gold coins because he knows no one else will offer him anything better than this. He promises Pirate 2 three gold coins if he votes for his plan and offers nothing to Pirates 1 and 3.
Pirate 3 realizes that he won’t get anything if he votes for Pirate 4’s plan, so he comes up with his own plan. He suggests that he gets 98 gold coins and offers Pirate 1 one gold coin in exchange for his vote. Pirates 2-4 would not receive any gold coins under this plan.
Pirate 2 is in a tricky spot. He can either vote for Pirate 4’s plan and get three gold coins or vote for Pirate 3’s plan and get nothing.
However, he realizes that if he votes for Pirate 3’s plan, there will be a tie between the two plans, and Pirate 5 will cast the deciding vote. In this case, Pirate 5 would choose Pirate 2’s plan since it offers him one more gold coin than the other two plans.
Pirate 1 knows that he won’t get anything if he votes for Pirate 3’s or Pirate 4’s plans, so he decides to come up with his own plan. He suggests that he gets one gold coin, Pirates 2-4 each get zero gold coins, and Pirate 5 gets all the remaining gold coins.
This plan is clever because it ensures that at least one pirate gets something instead of nothing if the other plans fail to receive a majority of votes.
In summary, the game theory behind the Pirate Game involves each pirate trying to maximize their share of the treasure while also trying to stay alive. The game also involves strategic voting based on seniority and the number of pirates involved. The game is not only interesting but can also help us understand how individuals make decisions in real-life situations where there are multiple stakeholders involved.
Game theory is a fascinating subject that has numerous applications in various fields. The Pirate Game is an entertaining example of game theory that involves pirates and their treasure.
The game highlights how individuals strategically make decisions based on their self-interest and the interests of others. By understanding the principles behind game theory, we can better understand how individuals make decisions in real-life situations.