PLEASE CHECK THIS HOW TO SOLVE Suppose that two candidates competing for political office must each choose a position fromthe set Sį = {1,2,..., 10}. Voters are equally distributed across these ten positions, andvote for the candidate whose position is closest to their own. If the two candidates areequidistant from a given position, the voters at that position split their votes equally. Eachcandidate wants to maximize their share of the total vote. Thus, for example, u₁(8,8) = 50and u₁(7,9) = 75. Note that you do not need to write out the payoff matrix to answer eitherof the following questions.(a) What strategies are strictly dominated for each candidate? Give a full explanation foryour answer; in particular, for each dominated strategy, be sure to explicitly identify atleast one other strategy that dominates it.Solution: Strategy 1 is strictly dominated by strategy 2 for each candidate. To seethis, note first that if the other candidate chooses position 1, then 2 gives a payoff of 90whereas 1 gives a payoff of 50. If the other candidate chooses position 2, then 2 gives apayoff of 50 whereas 1 gives a payoff of 10. If the other candidate chooses a position 3or higher, then position 2 always gives a payoff greater by 5 than that from position 1.Since position 2 gives a strictly higher payoff than position 1 against every strategy forthe opponent, position 1 is strictly dominated. Similarly, strategy 10 is strictly dominatedby strategy 9. No other strategies are strictly dominated since each is a best response tothe opponent choosing a position one spot farther from the median.(b) What strategies remain after iterated elimination of strictly dominated strategies?Solution: Once positions 1 and 10 have been eliminated for both players, position 2 isstrictly dominated by position 3 and position 9 is strictly dominated by position 8 (theargument is similar to the one given in part (i)). Once positions 2 and 9 have beeneliminated, position 3 is strictly dominated by position 4, and 8 by 7. Once 3 and 8 havebeen eliminated, 4 is strictly dominated by 5, and 7 by 6. We are left with strategies5 and 6 for each player, neither of which strictly dominates the other in the remaininggame.

In game theory, a dominating strategy is one in which a single approach is the best for a player…

he set S; = {1,2,..., 10}. Voters are equally distributed across these ten positions, and ote for the candidate whose position is closest to their own. If the two candidates are quidistant from a given position, the voters at that position split their votes equally. Each andidate wants to maximize their share of the total vote. Thus, for example, u₁(8,8) = 50 nd u₁(7,9) = 75. Note that you do not need to write out the payoff matrix to answer either f the following questions.

he set S; = {1,2,..., 10}. Voters are equally distributed across these ten positions, and ote for the candidate whose position is closest to their own. If the two candidates are quidistant from a given position, the voters at that position split their votes equally. Each andidate wants to maximize their share of the total vote. Thus, for example, u₁(8,8) = 50 nd u₁(7,9) = 75. Note that you do not need to write out the payoff matrix to answer either f the following questions.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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