Simultaneous Play Games Homework 1 Game Theory Economics 3208 Prof. V. Knoblauch This is a group homework assignment. I will assign each problem to a single group. Groups will present their solutions during class. You must work as a group and each member of the group must contribute during the presentation to receive credit. Although you are working as a group, I will grade each person individually. Of course, not everyone will have a chance to lead the group on every attempt and not everyone will get the answers correct on each attempt, that does not mean that you can't receive an A for this part of the assessment. There will be plenty of chances for students to contribute. Each group needs to work with only one solution sheet. But, I will leave the details of the presentation to you. 1. Another Example of Prisoners' Dilemma: Diplomatic Prisoners' Dilemma. Two Super Powers (Country 1 and Country 2) are each capable of developing WMD (weapons of mass destruction). They enter into a treaty banning the development of the new weapon. Each must now decide whether to honor the treaty (cooperate) or develop the weapon in secret (defect). If both cooperate the world is safe and at no cost: each wins 10 points. If they both defect the world is somewhat safe (mutual deterrence) but it is costly to build WMD, so they win 5 points each. If one of the players cooperates and and the other defects the cooperator is subject to bullying and perhaps loss of territory, that player wins 2 points. The defector is safe and may gain some territory. This leads to a big payoff of 12 points. a. List the the players. b. What are the strategies for each player? What are the strategy sets for each? c. Put the game in normal (bimatrix) form. Use the two prisoners' dilemma games you have seen as a template. In your matrix (C,C) should be the cell of the top row, first column of the matrix and so on. d. There are four candidates for a pure strategy Nash equilibrium. Show which ones are Nash and which ones are not using the a. the underlining method and b. the definition method