Consider the following public goods game: there are two consumers: Alice and Beth or {A, B}....

 

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Consider the following public goods game: there are two consumers: Alice and Beth or {A, B}. There are two goods, x and y, which they can spend time on, subject to the time constraint x₁ + yi ≤ 36 for i E {A, B} Utilities are given by uA = A +6√yA+ ayB₁ UB=XB +6√√YB + ByA where a, ß = [0, 1] Let a = B = 1. You may use, without proof, that the best response of Alice is YA = max {9 - YB, 0}. Find all Nash Equilibria. (3 marks) Let a = B = 1. Assume that if players disagree, they play the symmetric Nash Equilibrium. Find the Pareto Set and use this to put the scenario into the form of a bargaining problem: define a pair (S, d) where S is the set of feasible utility pairs and d is the disagreement point. (7 marks) Consider the (S, d) pair found in part (d). Discuss what happens under (i) the Nash Bargaining Solution, (ii) the ultimatum game where Alice is proposer. (5 marks) Consider the following public goods game: there are two consumers: Alice and Beth or {A, B}. There are two goods, x and y, which they can spend time on, subject to the time constraint x₁ + yi ≤ 36 for i E {A, B} Utilities are given by uA = A +6√yA+ ayB₁ UB=XB +6√√YB + ByA where a, ß = [0, 1] Let a = B = 1. You may use, without proof, that the best response of Alice is YA = max {9 - YB, 0}. Find all Nash Equilibria. (3 marks) Let a = B = 1. Assume that if players disagree, they play the symmetric Nash Equilibrium. Find the Pareto Set and use this to put the scenario into the form of a bargaining problem: define a pair (S, d) where S is the set of feasible utility pairs and d is the disagreement point. (7 marks) Consider the (S, d) pair found in part (d). Discuss what happens under (i) the Nash Bargaining Solution, (ii) the ultimatum game where Alice is proposer. (5 marks)