5 Pirates and 100 Gold Coins Puzzle 2 | Puzzle Interview

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5 Pirates and 100 Gold Coins Puzzle

There are 5 pirates (in strict order of seniority A, B, C, D and E) who found 100 gold coins. They must decide how to distribute them.

Rules of distribution are:

  1. The most senior pirate proposes a distribution of coins.
  2. The pirates, including the proposer, then vote on whether to accept this distribution. 
  3. If the majority accepts the plan, the coins are distribution and the game ends.
  4. If the majority rejects the plan, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.
  5. The process repeats until a plan is accepted or if there is one pirate left.
  6. In case of a tie vote, the proposer has the casting vote. ( A casting vote is a vote that someone may exercise to resolve a deadlock.)

Rules every pirate follows.

  1. Each pirate wants to survive.
  2. Given survival, each pirate wants to maximize the number of gold coins each receives.
  3. Each pirate would prefer to throw another overboard if all other results would otherwise be equal.

What is the maximum number of coins that pirate A might get?

Solution:

Pirate A will get the maximum coin: 98

So, Let try to find, how Pirate A figure it out.

Because E, has the most outcomes to consider, so let’s start by following E thought process.

  1. Suppose A, B and C die, only D and E are left. Since D is senior to E, he has the casting vote;
    so, D would propose to keep 100 for himself and 0 for E.

  2. If there are three left (C, D and E), C knows that D will offer E 0 in the next round; therefore, C has to offer E one coin in this round to win E’s vote.
    Therefore, when only three are left the allocation is C:99, D:0, E:1.

  3. If B, C, D and E remain, B can offer 1 to D; because B has the casting vote, only D’s vote is required.
    Thus, B proposes B:99, C:0, D:1, E:0.

  4. With this knowledge, A can count on C and E’s support for the following allocation, which is the final solution:

    A: 98 coins
    B: 0 coins
    C: 1 coin
    D: 0 coins
    E: 1 coin

The pirate game involves some interesting concepts from game theory.

One is the concept of common knowledge, where each person is aware of what the others know and uses this to predict their reasoning.

And the final distribution is an example of a Nash equilibrium, where each player knows every other players’ strategy and chooses theirs accordingly.

Even though it may lead to a worse outcome for everyone than cooperating would, no individual player can benefit by changing their strategy.

References: Pirate game – Wikipedia


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