Answer to Question #254754 in Microeconomics for selah

Question

Three pirates (in order of seniority A, B, C) find a treasure chest containing 100 (indivisible) coins. They have the following rules regarding the distribution of treasure. The most senior pirate on the ship proposes a plan of how to distribute the coins, and everyone takes a vote on the plan. If there are at least as many votes in favor as against, the vote passes and distribution is done accordingly. If the majority votes against, the proposer is thrown overboard, after which the now most senior pirate makes a proposal. Pirates prefer more coins to less. If a pirate is indifferent between voting for or against in terms of coins, he prefers throwing the proposer overboard. Find the sub-game perfect Nash equilibrium of this game. Hint: use backward induction and read carefully. 

Answer 1

 When each of the pirates votes, they think about the current proposal and other outcomes down the line. The order of seniority is known in advance so each of them can accurately predict how the others might vote in any scenario. This becomes apparent if we work backwards.

The final possible scenario would have all the pirates except C thrown overboard. Since B is senior to C he has the casting vote; so, B would propose to keep 100 coins for himself and 0 for C.

 If C throws B overboard ,he would get the whole amount of the coins from B