PART III: PROBLEM SOLVlNG/SHORT ESSAY (60 total points; 4 questions; variable points/question). Please answer all identied sub-questions. Please Show all of your work. It is necessary but not sufcient to state the correct answer. Partial credit for incomplete answers is given. Expand the space between questions as needed. 17. The zero-sum tennis game with pure strategies between Navratilova and Evert described b this matrix: NAVRRTILOVA has no Nash equilibrium. However, if mixed strategies are added to this game, a Nash equilibrium emerges. (a) Why is there not a Nash equilibrium for the game described by the above matrix? Explain. (b) Why is there a Nash equilibrium for the same game if mixed strategies are added? Explain. (c) Will adding mixed strategies to any zero-sum game with pure strategies always change the game from one for which there is no Nash equilibrium to one for which there is a Nash equilibrium? Why or why not? Explain. (15 total points) 18. I claimed in Lectures #23 and #25 that while calculating a best response point for a mixed strategy zero-sum game is a mathematical achievement, such a best response point is unlikely to be considered by a player who uses a mixed strategy decision procedure during that game. Call this claim 'D'. (a) What is the argument for D? (b) What, if any, considerations increase the likelihood that D is false? (10 total points) 19. Describe the differences between deterrent conditional strategic moves and compellent conditional strategic moves by doing the following: (a) Define 'deterrent' and 'compellent' (b) Explain why deterrents are typically threats and compellents are typically promises (c) Describe why making a threat or promise credible is important (d) Describe two or more distinct countermoves to deterrents and compellents. (20 total points) 20. Consider Dixit, Chapter 9, Problem U3, page 366-367. For those of you using the 4'\" edition rather than the 5'h edition, this problem is Chapter 8, Problem U4, page 330: In your own words, please complete parts (a) and (b) of this problem, making sure that your explanations are clear and comprehensive. (15 total points)