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4. Consider the following collective action game. Suppose you are a farmer. Your neighbor farmer and you can both benefit by constructing an irrigation project. The two of you can join together to do this, or one might do so on his own. Once the project has been constructed, the other automatically gets some benefit from it. The costs and benefits associated with building the irrigation project depend on which players participate. Suppose each of you can complete the project in 7 weeks, whereas if the two of you acted together, it would take only four weeks of time from each. The two-person project is also of better quality; each farmer gets benefits worth of six weeks' of work from a one-person project, and eight weeks' worth of benefit from a two-person project. The farmers decide simultaneously whether to work toward the construction of the project. The payoff table of the game is given below: YOUR NEIGHBOR Build Not Build 3.3 -1,5 You Not 5,-1 0,0 (a) What is the equilibrium outcome of this game? Is it the best outcome for both players? Does this game fit the description of a classical normal form game (prisoners' dilemma, battle of the sexes, chicken, coordination game)? If yes, which one? Explain. (b) Now suppose that the irrigation system requires major maintenance every year, so this situation can be viewed as a repeated game. Suppose the game is repeated for 5 years only (since both you and your neighbor are leasing the land, and you both plan to quit farming once the lease expires). game? Explain. What is the Subgame Perfect Nash Equilibrium of this finitely repeated (c) Now suppose the game is repeated infinitely often (maintenance is re- quired every year, and neither you nor your neighbor have plans to quit). Show that each player choosing "Build" every year can be supported as a Nash equilibrium of this infinitely repeated game, provided the players are patient enough (i.e., their discount factors are high enough). What is the minimal value of the discount factor that would allow to sustain (Build, be used to support this equilibrium? Build) as an equilibrium outcome in every period? What strategies can