9 Game Theory and Oligopoly

9 Game Theory and - Game Theory and Oligopoly Oligopoly is a market structure characterized by A few large firms that each have some market power

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Game Theory and Oligopoly
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Oligopoly is a market structure characterized by: - A few large firms that each have some market power. - Products that are homogeneous. - Firms are price-setters. - Examples include steel, oil, sugar etc. Let’s consider a market that is a duopoly : 2 firms.
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Example Market demand is given by p = 100 – y Each firm can produce at a constant cost of $40 per unit, that is MC = 40 And thus ATC = 40 $40 is the firm’s unit cost of production .
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We also assume that there are no other relevant costs and the oligopolists are established firms. First, let’s find the standard monopoly solution if there was only 1 firm serving the market: MR = 100 – 2y. Setting MR = MC, 100 – 2y = 40 y = 30 p = 100 – y = 100 – 30 = 70 Π = TR – TC = 70(30) – 40(30) = $ 900
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Now, let’s suppose that each firm either chooses to produce a small quantity of output, S = 15 or a large quantity of output, L = 20. If each firm chooses S = 15, total market output will be 15 + 15 = 30, the monopoly outcome. The firms will split the monopoly profit, each making a profit of $450.
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If each firm chooses to produce L = 20, total output will be 40, price will be p = 100 – 40 = 60. Total profit will be Π = 60(40) – 40(40) = 800 The firms will each make a profit of $400 If one firm chooses S = 15 and the other chooses L = 20, total market output will be 35, price will be p = 100 – 35 = 65 The firm producing S = 15 makes a profit of Π = 65(15) – 40(15) = $375 The firm producing L = 20 makes a profit of Π = 65(20) – 40(20) = $500
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We can set this situation up as a prisoner’s dilemma: 500, 375 400, 400 450, 450 375, 500
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Regardless of what Firm 1 does, Firm 2’s best response is to produce L = 20. Its profit will be either $500 ( > $450) or $400 (> $375). Firm 1 has the same dominant strategy, The outcome is a Nash equilibrium at (L , L) and profit = (400, 400). Yet, if they could agree to restrict their individual outputs to 15 units apiece, each could earn $450.
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Oligopolists have a clear incentive to collude or cooperate. If they agreed to both produce S, their profits would be maximized. However, oligopolists have a clear incentive to cheat on any simple collusive or cooperative agreement. If they agreed to produce S, either firm could cheat and produce L and increase its profit. Any agreement they make is not self-enforcing. When an agreement is a Nash equilibrium, it is self-enforcing: there’s a clear incentive to follow through.
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The Cournot Duopoly Model Now, let’s assume that our firms can produce any level of output. The Cournot model assumes:
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This note was uploaded on 06/18/2011 for the course ECON 2X03 taught by Professor Jamesbruce during the Fall '10 term at McMaster University.

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9 Game Theory and - Game Theory and Oligopoly Oligopoly is a market structure characterized by A few large firms that each have some market power

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