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Quiz 26. GT2

# Quiz 26. GT2 - player 3 the matrix player Fill in the poll...

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Shomu Banerjee ECON 201 CAMPAIGN GAME QUIZ Three candidates are in the running for an election. Each candidate has one unit of effort that s/he can spend on running a positive campaign or a negative campaign directed at one of the other candidates; a candidate cannot simultaneously run a positive and a negative campaign, or simultaneously run two negative campaigns. Poll ratings, r , are determined by the allocation of effort by all candidates according to the following formula: r = v i + p + n 2 where v i is a candidate’s current poll rating, p = 1 if s/he runs a positive campaign and zero otherwise, and n is the total number of negative campaigns run by others against person i . Assume that v 1 = 2, and v 2 = v 3 = 0, so candidate 1 is the current frontrunner with candidates 2 and 3 tied in second position. (a) In the matrices below, player 1 is the row player, player 2 the column player and

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Unformatted text preview: player 3 the matrix player. Fill in the poll ratings for each player in the matrices below: (b) The payoff for each person is given by the probability of being elected, not by the rating. Suppose that the probability of being elected is 1 if a candidate’s poll-rating is the highest, 1/2 if there are two candidates tied for first place, and 1/3 if all three are tied. Based on the poll-ratings you calculated above, fill in the payoffs for each player in the matrices on the next page. p n 1 n 3 p n 2 n 3 p n 1 n 3 p n 2 n 3 p n 1 n 3 p n 2 n 3 1 2 1 1 2 2 3 p n 1 n 2 (c) Find all the Nash equilibria of this game. p n 1 n 3 p n 2 n 3 p n 1 n 3 p n 2 n 3 p n 1 n 3 p n 2 n 3 1 2 1 1 2 2 3 p n 1 n 2...
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Quiz 26. GT2 - player 3 the matrix player Fill in the poll...

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