1.5. Explain why the simple majority method satisfies:(a) anonymity,(b) neutrality, and(c) monotonicity.

Individual A Cooperate Defect Individual B Cooperate 28, 28 34,8 Defect 8, 34 12, 12 Suppose individuals live in villages that are homogeneous by type and a fractions of their interactions takes place in their village, the rest occurring in the city where the types were mixed. The fraction of the population who are cooperators is a. a) Write the expected return functions for cooperate and defect as a function of s and a. b) Under which conditions does an interior equilibrium exist for the fraction of the population playing cooperate (a) c) If the interior equilibrium for a exists, is the interior equilibrium unstable or stable? d) Find the impact of higher s on the interior equilibrium for a. What intuitively does this outcome mean? Discuss your answer.

Firm 1 and Firm 2 compete in the same product market by setting quantities q₁ and 92, respectively. They have the same marginal cost c₁ = C₂ = 40. The market demand is p=1240 Q, where Q = 91 +92. 19. Suppose the game is played for one period. What are the equilibrium quantities? (a) q₁ = 1000, 92 1000 (b) q₁ = 800, q2 = 800 (c) 91 = 600, q2 = 600 (d) 9₁ = 400, q2 = 400 (e) 9₁ = 200, q2 = 200 In questions 19-21, suppose that this game is repeated for infinitely many periods. Firms have the same discount rate 8. Consider the situation in which the two firms are trying to implement a collusion scheme. With this intent, they employ the following grim-trigger strategy: in the first period, each firm produces the collusion quantity; from period two onwards, the firm keep producing the collusion quantity as long as no firm has ever pro- duced any quantity other than the collusion quantity; otherwise, the firm plays the Nash Equilibrium of the stage game. As you will see, what varies from one…

(b) Two hotels, Hotel Sandy and Hotel Magda, are competing for a limited number of tourists. The hotels have approval to either expand hotel operations, or add recreational water sports to their offerings. No one hotel has approval do both of these changes. A research company has determined that the following outcomes are likely: If Hotel Sandy expands, and Hotel Magda adds water sports, Hotel Sandy will increase its market share by 1%, and Hotel Magda will increase its market share by 3%. If Hotel Sandy adds water sports, and Hotel Magda expands, Hotel Sandy will decrease its market share by 5%, and Hotel Magda will increase its market share by 2%. If both hotels add water sports, Hotel Sandy will increase its market share by 4%, and Hotel Magda will increase its market share by 5%. If both hotels expand, Hotel Sandy will increase its market share by 2%, and Hotel Magda will decrease its market share by 5%. Given that both hotels employ game theory, what course of action would each…