Question

BONUS QUESTION: There are 5 rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them. The pirates have a strict order of seniority: A is superior to B who is superior to C, who is superior to D, who is superior to E. The pirate world's rules of distribution are thus that the most senior pirate coins. The pirates, including the proposer, then vote on whether to accept this distribution. In case of a tie vote the proposer has the deciding vote. If the distribution is accepted, the coins are disbursed and the game ends. If not, 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. Pirates base their decisions on three factors. a. First of all, each pirate wants to survive. b. Second, given survival, each pirate wants to maximize the number of gold coins he receives. c. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal. The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from the main proposal. (7 points)

Answer 1

solving the Game via Backward Induction.al The smallest proper subfame is when only 21 pirates I left, E proposes of all other are killed, so e will keep everything for him, E=100 Casa Now moving backwards, D&E are left I will propose & has deciding vote, If even E Rejects, still D's proposal will win, he will keep everything for him, D: 100, E:0 can bribe & e Rejects, then Nexo, when 3 pirates, c will propose, & E pirate, Boz E will support it, as if D will give him Nothing, 80 c proposes qq coins for him & - C. 99 , Dao E: 1 ¥ for € Bribe D, 4 pilates, then B will be proposes wil B; 99, CO, 0° 1, 2:0 5 eis ates, H will be proposer Needs majority to get its proposal passed, A: 98, 8.0, 0:4, D: 0, 2:1 SPNB allocation A Keeps 98 coins with him b offers icon each to C&E