1. Two players have to split a dollar. There are two periods. In the first period, player 1 makes an offer on how to divide the dollar; then player 2 decides whether to accept or reject the offer; if player 2 accepts the offer, they split the dollar as accorded, and the game ends; if player 2 rejects the offer, then they move to the second period. In the second period, player 2 gets to make an offer on how to split the dollar; if player 1 accepts, they split the dollar as accorded; if player 1 rejects the offer, nobody receives any share of the dollar, and the game ends. Assume both players have a discount factor of 8. Assume also that when indifferent, a player accepts the proposal.
(a) Draw the game tree.
(b) Find the SPNE.
2. A non-governmental organization (NGO) operating in the United States estimates that the foreign aid flowing from the U.S. to developing coun- tries is not helping the poor in those countries. The NGO is consider- ing the two following actions to help improve this situation. Evaluate whether either of these actions is likely to achieve its goal. In formu- lating your answers, assume that the Selectorate model of foreign aid is a good description of how foreign aid works.
(a) Educating the policy makers in the U.S. on the fact that current foreign aid is primarily going to dictators and is not then being used by those dictators to help their people.
(b) Trying to persuade American voters to care more about the poverty and suffering of people in the developing world than the policy concessions their leaders can make to the US and to vote based on whether their government pursues a policy that actually achieves that goal.
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