Question

strategies. 15.2-7. Two politicians soon will be starting their campaigns against each other for a certain political office. Each lect the main issue she will emphasize as the theme of her cam- paign. Each has three advantageous issues from which to choose, but the relative effectiveness of each one would depend upon the issue chosen by the opponent. In particular, the estimated increase in the vote for politician 1 (expressed as a percentage of the total vote) resulting from each combination of issues is as follows: must now se- er. Issue for Politician 2 ng 3 3 -1 7 Issue for 2 2 Politician 1 3 -1 -3 -5 However, because considerable staff work is required to research and formulate the issue chosen, each politician must make her own choice before learning the opponent's choice. Which issue should she choose? 4 For each of the situations described here, formulate this prob- lem as a two-person, zero-sum game, and then determine which issue should be chosen by each politician according to the speci- fied criterion. a) The current preferences of the voters are very uncertain, so each additional percent of votes won by one of the politicians has the same value to her. Use the minimax criterion. b) A reliable poll has found that the percentage of the voters cur- rently preferring politician 1 (before the issues have been raised) lies between 45 and 50 percent. (Assume a uniform dis- tribution over this range.) Use the concept of dominated strate- gies, beginning with the strategies for politician 1. (c) Suppose that the percentage described in part (b) actually 45 percent. Should politician 1 use the minimax criterion? Explain. Which issue would you recommend? Why? r. e y : d were

Answer 1

Solu tion: civen the data matsix payoff 04 the game Politichane) in 2. 1 -3 -5 max 7 min (1,0,3) O (-yo5)O man v -O mint max ) mox(min) y o stsictly detominable gama Tt is Value of 9ame - optimum stokegy(2,2).