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9. Gamma, Delta, and Epsilon are three robots who share an apartment. They get really hot in the summer and are considering buying a window air conditioner to cool the apartment's common area. There are three different quality AC units available: "High" quality costs $1,000, Medium costs $400, and Low costs $ 100. The three robots have identical preferences. The robots' willingnesses to pay for the different quality units are $300, $200, and $0, respectively. (a) From the point of view of efficiency (maximization of total surplus), should they buy one of the units? If so, which one? (b) Consider the following voting procedure for financing the AC unit purchase: each robot writes down on a piece of paper its name, and the quality of the AC unit it wants. The unit that receives the most votes is bought, and its cost is split equally among those who voted for it. Describe the problems with this mechanism when the efficient AC unit receives unanimous support. What if it receives only two votes? (Analyze whether or not each of these outcomes is a Nash equilibrium, and how the "free rider" problem may show up.) 9. Gamma, Delta, and Epsilon are three robots who share an apartment. They get really hot in the summer and are considering buying a window air conditioner to cool the apartment's common area. There are three different quality AC units available: "High" quality costs $1,000, Medium costs $400, and Low costs $ 100. The three robots have identical preferences. The robots' willingnesses to pay for the different quality units are $300, $200, and $0, respectively. (a) From the point of view of efficiency (maximization of total surplus), should they buy one of the units? If so, which one? (b) Consider the following voting procedure for financing the AC unit purchase: each robot writes down on a piece of paper its name, and the quality of the AC unit it wants. The unit that receives the most votes is bought, and its cost is split equally among those who voted for it. Describe the problems with this mechanism when the efficient AC unit receives unanimous support. What if it receives only two votes? (Analyze whether or not each of these outcomes is a Nash equilibrium, and how the "free rider" problem may show up.)

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