Seven goblins are deciding how to split 100 galleons. The goblins are named Alguff, Bogrod,… 1 answer below »

Seven goblins are deciding how to split 100 galleons. The goblins are named Alguff, Bogrod, Eargit, Griphook, Knadug, Ragnuk, and Uric, and they’ve been rank-ordered in terms of magical power, with Alguff the weakest and Uric the strongest. The game starts with Alguff, who proposes an allocation of the 100 galleons coins, where an allocation is an assignment of an amount from {0,1, …, 100} to each goblin and where the sum across goblins equals 100. All goblins then vote simultaneously, either “yea” or “nay,” on the allocation. If at least half of them vote in favor of the allocation, then it is made and the game is over. If less than half vote for the proposed allocation, then the other goblins perform a spell on Alguff and transform him into a house elf for a week. In that event, it is Bogrod’s turn to put forth an allocation for the remaining six goblins. Again, if at least half vote in favor, the allocation is made; if not, then Bogrod is made into a house elf for a week and it is Eargit’s turn. This procedure continues until either an allocation receives at least half of the votes of the surviving goblins or all but Uric have been transformed into house elfs, in which case Uric gets the 100 galleons. Assume that the payoff to a goblin is if he is made into a house elf and that it equals the number of galleons if he is not. Using the solution concept of subgame perfect Nash equilibrium, what happens? (Focus on subgame perfect Nash equilibria in which a goblin votes against an allocation if he is indifferent between voting for it and against it.)