there are 3 game theory question and 1 essay question
so total is 4 question
1.1 – Suppose y=1. What is the SPNE?
1.2 – Under what values of y is R part of a SPNE?
2) Contributing to a public good. Consider a game played by 10 people. The players all live in the same building, and would like to buy a Christmas tree to decorate the entrance to the building. The Christmas tree costs 2$. Each player can choose to contribute 0$, 1$ or 2$ towards purchasing the tree. The players must all choose simultaneously (i.e., all at the same time). Each player obtains a payoff of 3 if the tree is purchased, and pays a cost equal to the amount of his/her own contribution (i.e., if I contribute 1$ and the tree is purchased, my payoff is 3-1=2. If I contribute 1$ and the tree is not purchased, my payoff is -1). What are the NE of the game? (be careful! There can be many equilibria of the same form!)
3) Mauriland is a fictitious country with only two politically active groups. One group has more liberal inclinations, while the other group holds conservative values. The two groups must choose between a liberal candidate L and a more conservative candidate C to the highest position in office. If they do not coordinate on the same candidate, the constitution provides that the country be ruled by co-decision, which is historically known to lead to inefficient governance. Each group would like the candidate closer to their political preferences to win, but they also wish that only one candidate is chosen to the highest office. The preferences of the two groups are given by the 2×2 table below. Find the NE of this game.
Question 1 (ESSAY): What is the role of a political leader? When/why are political leaders successful?(Hint: remember the 3 models of leaders as agents, experts and coordinators)
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