NEED SOMEONE WHO IS ACTUALLY EXPERIENCED AND GOOD AT ECONOMICS. IF YOU ANSWER THIS QUESTION BUT HAVE NO IDEA WHAT YOU ARE DOING OR GIVING WRONG ANSWERS YOU WILL BE RATED POORLY! LOOKING FOR LEGITIMATE ECONOMIC HELP, NOT BS. ANSWERS MUST HAVE EXPLANATION AND/OR MATHEMATICAL LOGIC BEHIND IT.

1. Consider a strategic situation represented by the following payoff matrix: LR U 4,4 1,5 D 5,1 0,0 (a) Find all Nash equilibria (pure and mixed). What are the payoffs from these equilibria? (b) Suppose the game is played twice. At the end of the first period, the action choice of each player is commonly observed. Is there a subgame perfect equilibrium (possibly in mixed strategies) where U, L is played in the first period? If yes, describe the strategies. If no, explain why not. (c) Now consider an infinitely repeated version where action choices are commonly observ- able after each stage. Each player discounts the future at rate 8. i. What is each player's payoff if they were to play U, L every period? ii. Describe grim trigger strategies such that if they form an SPE, in that SPE the players play U, L every period. (Hint: note that (D,R) is not a NE of the stage game. Think about which stage game NE could be considered a punishment for player 1. How about for player 2?) iii. What is the condition on that guarantees that neither player is willing to deviate from the strategies you described above? 1. Consider a strategic situation represented by the following payoff matrix: LR U 4,4 1,5 D 5,1 0,0 (a) Find all Nash equilibria (pure and mixed). What are the payoffs from these equilibria? (b) Suppose the game is played twice. At the end of the first period, the action choice of each player is commonly observed. Is there a subgame perfect equilibrium (possibly in mixed strategies) where U, L is played in the first period? If yes, describe the strategies. If no, explain why not. (c) Now consider an infinitely repeated version where action choices are commonly observ- able after each stage. Each player discounts the future at rate 8. i. What is each player's payoff if they were to play U, L every period? ii. Describe grim trigger strategies such that if they form an SPE, in that SPE the players play U, L every period. (Hint: note that (D,R) is not a NE of the stage game. Think about which stage game NE could be considered a punishment for player 1. How about for player 2?) iii. What is the condition on that guarantees that neither player is willing to deviate from the strategies you described above