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Three oligopolists operate in a market with inverse demand given by P(Q) = a - Q, where Q=91+92 +93 and q; is the quantity produced by firm i

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Three oligopolists operate in a market with inverse demand given by P(Q) = a - Q, where Q=91+92 +93 and q; is the quantity produced by firm i. Each firm has a constant marginal cost of production, c, and no fixed cost. The firms choose their quantities as follows: (1) firm 1 chooses q? > 0; (2) firms 2 and 3 observe q? and then simultaneously choose 42 and 43, respectively. What is the sub game-perfect outcome? Exercise 2 The simultaneous-move game (below) is played twice, with the outcome of the first stage observed before the second stage begins. There is no discounting. Can the payoff (4,4) be achieved in the first stage in a pure-strategy sub game-perfect Nash equilibrium? If so, give strategies that do so. If not, prove why not. Player 2 LC R T (3, 1) (0,0) (5,0) Player 1 M (2,1) (1.2) (3,1) B (1.2) (0.1) (4,4) Exercise 3 What is a strategy in a repeated game? What is a subgame in a repeated game? What is a subgame-perfect Nash equilibrium?