Competitive Markets, non Competitive Markets, Game Theory

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timer Asked: Jan 20th, 2021

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Answering the questions with brief answers.

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You can sell the goods separately, in a pure bundle or in a mixed bundle. (If indifferent between two options, assume consumers choose the alternative which maximizes the firm's profit). • Which strategy would maximize the profit of the firm? (A detailed answer is expected, show the steps of your reasoning). Exercise 3 Consider the following game: a b с A 0,11.5 0,0 10,10 B 0,0 6,6 0,0 C 4,4 0.0 11.5, 0 1. Find all the Nash equilibria of the stage game. Express the resulting payoffs. Suppose the game is played twice and the discount factor is d = 1. Players observe the actions chosen in the first play of the game prior to the second play. 2. Can you propose a Subgame Perfect Nash Equilibrium where players get 10 in the first period? Show that it is an equilibrium. Suppose the game is played twice and the discount factor is d = 1/2. 3. Can you propose a Subgame Perfect Nash Equilibrium where players get 10 in the first period? Exercise 1 Use successive elimination of dominated strategies to solve the following game. Explain the steps you followed. Left Middle Right (4,3) (2,7) (0,4) Down (5,0) (5, -1) (-4,-2) Up Exercise 2 Consider the following game: Left Middle Right Top (4,2) (?,2) (3,1) Middle (3,5) (2,?) (2,3) Bottom (2,3) (3,4) (4,2) 1. Complete the payoffs of the game table above so that Player 2 (column player) has a dominant strategy. State which strategy is dominant. (Note: there are many equally correct answers.) 2. Complete the payoffs of the game table above so that neither player has a dominant strategy, but also so that each player does have a dominated strategy. State which strategies are dominated and state by which strategy it is dominated. (Again, there are many equally correct answers.) 1 Exercise 3: Air Strike Army A has a single plane with which it can strike one of two possible targets. Army B has one anti-aircraft gun that can be assigned to one of the targets. The value of target 1 is 1 and the value of target 2 is 2. Army A can destroy a target only if the target is undefended and A attacks it. Army A wishes to maximize the expected value of the damage and army B wishes to minimize it. If Army A attacks a defended target, both payoffs are 0. Players move simultaneously. 1. Express the normal form of the game (Payoff table) 2. Find the Nash equilibrium.
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