2. \"Not Survivor\". [This question was on the 2001 nal exam] Six former 159a students Ann, Bob, Carl, Dora, Ed, and Fran are the contestants in a new \"real TV\" show. They are placed on an island. The rules of the game are as follows. Ann goes rst. She is given a bag that everyone knows contains six gold coins. Ann makes a proposal of how to allocate the six coins among the six contestants including herself. The contestants (including Ann) then vote 'yes' or 'no' on the proposal. If the proposal gets more than half the votes then the coins are allocated according to the proposal and everyone leaves the island. If the proposal gets half or fewer than half the votes then Ann has to leave the island empty-handed and she is out of the game. In this case, the bag of six gold coins passes to Bob. He gets to make a proposal of how to allocate the coins among the remaining contestants (i.e., including Bob but excluding Ann) and the remaining contestants (i.e., including Bob but excluding Ann) then vote. As before, if the proposal gets more than half the votes then the coins are allocated according to the proposal and everyone leaves the island. If the proposal gets half or fewer than half the votes then Bob has to leave the island empty-handed and is out of the game. In this case, the bag of six gold coins passes to Car]. And so on, with the same voting rules, with each failed proposal leading to expulsion of the proposer, and with the role of proposer being passed on alphabetically. The following assumptions matter. The coins are indivisible, there is no other money on the island, and side contracts to make payments off the island are not allowed. There are no abstentions; each surviving voter must vote yes or no: whenever a voter is indterent, she or he votes no. The players only care about the gold (and this is common knowledge). For example, leaving empty handed because your proposal fails is the same as leaving empty-handed because a successful proposal gives you no coins. Finally: it is common knowledge that all the contestants were well trained in Game Theory at Yale. What proposal should Ann make and why