Suppose Tokyo and Berlin will have either good luck or bad l…

Suppose Tokyo and Berlin will have either good luck or bad luck (each with equal chance) in earnings the coming year. If their luck is negatively correlated, they can set an arrangement to pool their income and split evenly in order to decrease the risk they’re exposed to.

Suppose an amusement park is being built in a city with a po…

Suppose an amusement park is being built in a city with a population of 100. Voluntary contributions are being solicited to cover the cost. Each citizen is being asked to give $100. The more people contribute, the larger the park will be and the greater the benefit to each citizen. But it is not possible to keep out the non-contributors; they get their share of this benefit anyway. Suppose that when there are n contributors in the population, where n can be any whole number between 0 and 100, the benefit to each citizen in monetary unit equivalents is n2 dollars. Suppose that initially no one is contributing. You are the mayor of the city. You would like everyone to contribute and can use persuasion on some people. What is the minimum number whom you need to persuade before everyone else will join in voluntarily?

Consider an election with 4 candidates: Berlin, Tokyo, Denve…

Consider an election with 4 candidates: Berlin, Tokyo, Denver and Lisbon. There is a total of 5 voters for this election (A, B, C, D and E). The Professor has decided to conduct the election according to the instant runoff voting rules. Given the preferences of the voters (ranked 1 is most preferred, ranked 4 is least preferred), who wins the election?  

Consider a vote being taken by three roommates, A, B, and C,…

Consider a vote being taken by three roommates, A, B, and C, who share a triple dorm room. They are trying to decide which of three elective courses to take together this term. (Each roommate has a different major and is taking required courses in her major for the rest of her courses.) Their choices are Philosophy, Geology, and Sociology, and their preferences for the three courses are as shown here:   The roommates have decided to have a two-round vote and will draw straws to determine who sets the agenda. Suppose C sets the agenda and wants the Geology course to be chosen. How should she set the agenda to achieve this outcome if she knows that everyone will vote strategically in all rounds? In the first round, C should set up _____________.