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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.
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consider the three player game in question 2 in assignment 1. Assume now that player 3 moves first. Players 1 and 2
A game frequently displayed in tv police dramas. 2 partners in crime are separated into separate rooms at the police station and given an identical deal. If one implicates the oppo
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the first three words are ''''the boys'' down''''. what are the last three words?
Consider two quantity-setting firms that produce a homogeneous good. The inverse demand function for the good is p = A - (q 1 +q 2 ). Both firms have a cost function C = q 2 (a
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The following is a payoff matrix for a non-cooperative simultaneous move game between 2 players. The payoffs are in the order (Player 1; Player 2): What is/are the Nash Equil
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