Every year, on the Saturday before the Academy Awards, film enthusiasts Larry, Curly and Moe have...

 

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Every year, on the Saturday before the Academy Awards, film enthusiasts Larry, Curly and Moe have a movie marathon and mini awards show to decide on the 'Best Picture' of the previous year, fueled by a mutual love of movies and a lot of popcorn. This year, they decide on a shortlist of three movies that seem to be getting the most buzz: an action-adventure film packed with twists and turns, Adrenaline 1 Rush (which we'll denote by A); a dramatic, character-driven biopic, Born and Raised (B); and the dark, gritty crime thriller, Cops and Robbers (C). After watching and discussing all three movies, each person's preferences are as follows: Larry prefers A to B and prefers B to C. Curly prefers C to A and prefers A to B. Moe prefers B to C and prefers C to A. Since they seem to be stuck, they agree to have a vote. Here's how it will work. Each person writes their selection for best picture on a ballot. If one movie receives more votes than the others, it wins the award. If there is a three way tie in which each movie gets a single vote, then Larry (as the host) breaks the tie. (Note: Larry doesn't get to vote a second time in the case of a three way tie, but rather whatever film he had voted for already would be the winner.) We assume that all three movie lovers are perfectly rational, and that each knows the preferences of the other two; we would like to determine how each of them would vote, and which movie will take home the coveted prize. (a) (3 marks) For each individual, determine which of their strategies are strictly or weakly dominated. (b) (2 marks) After eliminating the strategy (or strategies) found in part a), which strategy/strategies can you now eliminate? What will be the result of the vote? ("...and the Oscar goes to....) 4. Corporate Division (5 marks total) There are five executives on the board of directors of a major financial corporation: a CEO and four vice-presidents. After a very profitable year, there is a surplus of 100 million dollars that is to be shared among the board members as bonuses. The CEO calls a meeting to decide how to split up the money. After some deliberation, they agree on the following procedure: Each board member will submit a proposal about how to divide the money, one after the other. Every year, on the Saturday before the Academy Awards, film enthusiasts Larry, Curly and Moe have a movie marathon and mini awards show to decide on the 'Best Picture' of the previous year, fueled by a mutual love of movies and a lot of popcorn. This year, they decide on a shortlist of three movies that seem to be getting the most buzz: an action-adventure film packed with twists and turns, Adrenaline 1 Rush (which we'll denote by A); a dramatic, character-driven biopic, Born and Raised (B); and the dark, gritty crime thriller, Cops and Robbers (C). After watching and discussing all three movies, each person's preferences are as follows: Larry prefers A to B and prefers B to C. Curly prefers C to A and prefers A to B. Moe prefers B to C and prefers C to A. Since they seem to be stuck, they agree to have a vote. Here's how it will work. Each person writes their selection for best picture on a ballot. If one movie receives more votes than the others, it wins the award. If there is a three way tie in which each movie gets a single vote, then Larry (as the host) breaks the tie. (Note: Larry doesn't get to vote a second time in the case of a three way tie, but rather whatever film he had voted for already would be the winner.) We assume that all three movie lovers are perfectly rational, and that each knows the preferences of the other two; we would like to determine how each of them would vote, and which movie will take home the coveted prize. (a) (3 marks) For each individual, determine which of their strategies are strictly or weakly dominated. (b) (2 marks) After eliminating the strategy (or strategies) found in part a), which strategy/strategies can you now eliminate? What will be the result of the vote? ("...and the Oscar goes to....) 4. Corporate Division (5 marks total) There are five executives on the board of directors of a major financial corporation: a CEO and four vice-presidents. After a very profitable year, there is a surplus of 100 million dollars that is to be shared among the board members as bonuses. The CEO calls a meeting to decide how to split up the money. After some deliberation, they agree on the following procedure: Each board member will submit a proposal about how to divide the money, one after the other.