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1. Suppose that two firms face the following payoff matrix: Firm 1 Low Price High Price Low Price Firm 2 High Price Given these payoffs, Firm 2 wants to match Firm 1's price, but Firm 1 does not want to match Firm 2's price. What, if any, are pure-strategy Nash equilibria of this game? What is the mixed-strategy Nash equilibrium for the game. [Hintz Static game] 2. Two firms are planning to sell 10 or 20 units of their goods and face the following profit matrix: Firm2 10 Firm 1 20 a) Draw the game tree ifFirm 1 can decide first. What is the outcome? 13) Draw the game tree ifFirm 2 can decide first. What is the outcome? 3. Suppose two identical firms, each with a marginal cost of $60 per unit, are competing in a market with demand Q 2 150 p. a) Find the equilibrium quantities for the firms and price if the firms collude (form a cartel). b) Find the quantities for the firms and price in Nash-Cournot equilibrium. c) Find the quantities for the firms and price in Stackelberg equilibrium when Firm 1 moves first. 4. The firms in a duopoly produce differentiated products. The inverse demand for Firm 1 is p1 = 52 q1 0.5q2. The inverse demand for Firm 2 is p2 = 40 q2 0.5q1. Each Firm has a marginal cost of $1 per unit. Solve for the Nash-Cournot equilibrium quantities