I. Problem 1: 30%). Two politicians are running against each other for the U.S. Senate. Cam- paign plans must now be made for the final two days, which are expected to be crucial because of the closeness of the race. Therefore, both politi cians want to spend these days campaigning in two key cities, Bigtowrn and Megalopolis. To avoid wasting campaign time, they plan to travel at night and spend either one full day in each city or two full days in just one of the cities. However, since the necessary arrangements must be made in advance, heither politician will learn his opponent's campaign schedule until after he has finalized his own. Therefore, each politician has asked his campaign manager in each of these cities to assess what the impact would be (in terms of votes won or lost) from the various possible combinations of days spent there by himself and by his opponent. He then wishes to use this information to choose his best strategy on how to use these two davs. To formulate this problem as a two-person, zero-sum game, we must identify the two players (obviously the two politicians), the strategies for each player, and the payoff table. As the problem has been stated, each player has the following three strategies: Strategy 1 = spend one day in each city Strategy 2 = spend both days in Bigtowm. Strategy 3 spend both days in Megalopolis. (a) [15%) Define (imagine) a payoff table in such a way that the problem can be fully solved using the concept of dominated strategies (b) [15%] Use the concept of dominated strategies to determine the best strategy for each side