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finalexamfall2003 - Your Name Final Exam 18 Dec 2003 Econ...

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1 Your Name: ____________________________ Final Exam: 18 Dec 2003 Econ 431 David Reiley You have 120 minutes to take this exam. There are a total of 100 points possible, plus three extra-credit questions (1f, 1g, 4g) worth a total of 20 points. Please make sure to pace yourself, so that you answer all questions, even incompletely. I do give partial credit for incomplete work, but I give zero credit for blank pages. In order to get partial credit in case you make an error, you will want to explain carefully what you are doing. 1) In the game show The Weakest Link, players take turns answering questions; each right answer adds to a pot of money for the group. After each round of questions, the players vote to remove one of their group from the game. A player who leaves the game receives zero prize money. When there are only two players left, there is one round of questions in which the two players again add to the pot with correct answers. Following this round, instead of a vote to determine the winner, the winner is determined by a final round of questions; whoever answers more questions correctly is the winner of the pot of money. An interesting question is whether it makes sense strategically for players to want to vote off the player who answers the fewest questions correctly, also known as the “weakest link.” For a simplified analysis of equilibrium behavior in this game, let’s consider what happens starting from the point where the final three players are choosing which one of them will be “voted off” the game. Suppose that at this point there is a pot of $1000 already accumulated. Suppose also that the three players have three different abilities in answering questions: player A has an ability of 0.9, Player B has an ability of 0.5, and Player C has an ability of 0.3. After the voting, each remaining player will manage to add to the pot an amount equal to $500 times her ability. (For example, if Players A and B remain, then the final pot will equal $1000 + 0.9($500) + 0.5($500), for a total of $1700.) After the final amount of the pot has been determined, suppose that in the final round the remaining player with the higher ability will win the entire pot, and the player with the lower ability will lose (earn a payoff of zero). In the voting game, each player may vote for one of the other two players. Voting is decided by a plurality rule. In case of a tie, the highest-ability player (the “strongest link”) gets to break the tie in her own favor.
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2 a) (5 points) There are three possible outcomes to this voting game. Either A gets eliminated, B gets eliminated, or C gets eliminated. For each of these three cases, compute the payoffs to the three players. Fill these amounts in to the following table.
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