Question

There are four thieves who have found 100 gold coins on a ship. they must decide how to distribute them. a distribution is only of whole coins, they cannot be sliced, diced, or melted. the thieves are ranked by seniority, thief 1 is the most senior, then thief 2, then thief 3, and then thief 4. the thieves operate by seniority. the most senior thief first proposes a distribution. the thieves, including the proposer, then vote whether to accept this distribution. if the majority accepts the plan or if there is a tie, then the coins are disbursed and the game ends. if a strict majority rejects the plan, then the proposer is thrown overboard from the ship, and the next most senior thief makes a new proposal. the process repeats until a plan is accepted or if there is only one thief left. the thieves' priorities are as follows: each thief wants to survive. given survival, each thief wants to maximize the number of gold coins he receives. each thief prefers to throw another overboard if all other results would otherwise be equal. in the spne:

thief 1 gets ______

Answer 1

In the optimal strategy for Thief 1, he gets 98 gold coins.

Thief 1 needs to propose a distribution that ensures his own survival, as well as gaining the approval of at least one other thief.

Thief 1 can propose to take 98 coins for himself and distribute 1 coin each to Thieves 2 and 3. This gives him the majority of coins and ensures the survival of Thieves 2 and 3.

Thieves 2 and 3 would likely vote in favor of this proposal since they are getting more than 0 coins and they also prioritize survival.

Thief 4 would vote against the proposal, but since Thieves 2 and 3 together form a majority, the proposal is accepted.

Thief 1 will get:

= 100 - 2

= 98