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Consider the electoral competition game presented in Lecture 6. In this game there are two candidates who simultaneously choose policies from the real line. There is a distribution of voters with median m and the candidate whose policy is closest to the median wins the election and the winning candidate's policy is implemented. If the two candidates are an equal distance from the median, then the average of the two policies is implemented. For this problem we suppose that both candidates care about both the implemented policy and winning the election. That is, the payo to each candidate has two parts. The first part is the utility from the implemented policy a*. That is, each candidate has utility u(a* ; xi), where xi is the ideal policy of candidate i and utility decreases to the left and right of xi. We suppose that xi < m < xj . The second part is the value of winning office, which we denote wi > 0 for candidate i. Putting these two parts together, we de ne the payoff to candidate i by
Find all Nash equilibria to this game.
Write two methods for the mouse trap game (using your board created in Assignment 3) and an event handler (another method) to test the two methods. 1. world.raise(item) where
a) Define the term Nash equilibrium b) You are given the following pay-off matrix: Strategies for player 1 Strategies for player 2
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Combining Simultaneous and Sequential Moves The material in this chapter covers a variety of issues that require some knowledge of the analysis of both sequential- move
GAME 1 Claim a Pile of Dimes Two players Aand B are chosen. The instructor places a dime on the table. Player A can say Stop or Pass. If Stop, then A gets the dime and the gam
Take a news story, old or recent, and analyze it from a game theoretic perspective. Provide a hard copy of the source of your news story and consult relevant game theoretic literat
Nineteenth century French economist attributed with the introduction of the theory of profit maximizing producers. In his masterpiece, The Recherches, published in 1838, Cournot pr
A reserve worth is that the minimum acceptable bid in an auction. If no bidder submits a bid higher than the reserve worth, the auctioneer keeps the item offered for sale. Alternat
GAME PLAYING IN CLASS There are several games that are appropriate for use on the first or second day of class. These games are simple but can be used to convey important poin
Backward induction is an iterative procedure for resolving finite general form or sequential games. First, one decides the finest policy of the player who makes the last move of th
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