Seven goblins are deciding how to split 100 galleons. The goblins are namedAlguff, Bogrod, Eargit, Griphook, Knadug, Ragnuk, and Uric, and they?vebeen rank-ordered in terms of magical power, with Alguff the weakest andUric the strongest. The game starts with Alguff, who proposes an allocationof the 100 galleons coins, where an allocation is an assignment of anamount from {0,1, . . . , 100} to each goblin and where the sum across gob-lins 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, thenit is made and the game is over. If less than half vote for the proposed allo-cation, then the other goblins perform a spell on Alguff and transform himinto a house elf for a week. In that event, it is Bogrod?s turn to put forth anallocation 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 aweek and it is Eargit?s turn. This procedure continues until either an alloca-tion receives at least half of the votes of the surviving goblins or all but Urichave been transformed into house elfs, in which case Uric gets the 100galleons. Assume that the payoff to a goblin is if he is made into ahouse elf and that it equals the number of galleons if he is not. Using the so-lution concept of subgame perfect Nash equilibrium, what happens? (Focuson subgame perfect Nash equilibria in which a goblin votes against an allo-cation if he is indifferent between voting for it and against it.)