introduction to the game theory

(25 points) Five pirates A, B, C, D and E, have a treasure of 100 (indivisihle) gold coins. Pirate A is older than B, who is older than C, who is older than D, who is older than E. The pirates on the boat have the following rule: The oldest pirate on-board proposes how to share the coins. All the pirates (including the proposer) vote. If 50% or more of the pirates vote in support of the proposal, then the coins are shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard and will be eaten by sharks. The procas is repeated with the remaining pirates on-board. A pirate that gets the same number of coins voting in favor or against a proposal will vote against it. The ve pirates are intelligent, rational, greedy, and do not wish to die. What would pirate A propose in a subgame perfect Nash equilibrium? Explain clearly