Two politicians soon will be starting their campaigns against each other for a certain politicaloffice. Each must nowselectthe main issue she will emphasize as the theme of her campaign.Each has three advantageous issues from which to choose, but the relative effectiveness ofeach one would depend upon the issue chosen by the opponent. In particular, the estimatedincrease in the vote for politician 1 (expressed as a percentage of the total vote) resultingfrom each combination of issues is as follows:
However, because considerable staff work is required to researc–h and formulate the issuechosen, ea. politician must rnake her own choice before learning the opponent’s choice.Which issue should she choose?
For each of the situations described here, formulate this problem as a two-person, zero-sum game, and then determine which issue should be chosen by each politician according to thespecified criterion.
a. The current preferences of the voters are very uncertain, so each additional percent ofvotes won by one of the politicians has the same value to her. Use the minimaxcriterion.
b. A reliable poll has found that the percentage of the voters .rtently preferringpolitician 1 (before the issues have been raised) lies between 45 and 50 percent.(Assume a uniforrn distribution over this range.) Use the concept , dominatedstrategies, beginning with the strategies for politician 1.
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c.Suppose thatthe percentage described in part (b) actually were 45 percent. Shouldpolitician 1 use the minimax criterion? Explain. Which issue would you recommend?Why?