1. Consider Hardin's (1963] model of rational herders' problem. You and your neighbors are both herders and you share a common pasture where your catde's can graze. Each of you receive a direct benet from your animals {more you can graze them. the better it is for your personal profit]. but both of you also suffer from delayed cost due to deterioration of the common pasture when yours' or your neighbors cattte's oyergraze. There are two strategies you and your neighbor can choose i} \"cooperate strategy" labeled as "C" (where you can your neighbor equally share resources] and ii) defect strategy "D" {This is when the player grazes as many cattle as she can for her self-interest. not really caring about her neighbor}. Here is how the payoffs are designed. If you and your neighbor both cooperate, both of you get 1Q profit points. If one of you cooperate and the other defects, then the one who cooperates will get -1 profit point and the one who defects will get 11 profit points. If both of you choose to defect [overgrazing], this depletes the resource quick enough such that you get a profit of H points. a. f. Based on the information above, label the branches of the tree correctly. in Figure 1. Y refers to you and N refers to your neighbor. Neatly express the mechanics of the game on a 2 by 2 matrix. Show the players, strategies, and respective outcomes as in lecture. Pick out your neighbor's dominant strategy. What is your dominant strategy? Given that both of you play your dominant strategy (which is usally what happens under the assumption that you are solely driven by self-interest], what is the equilibrium outcome? Is the equilibrium outcome in pan e pareto optimal? Explain