Oligopolies and Game Theory Lecture 5
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Oligopolies
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1. Market Stucture and Game Theory
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Oligopolies – two or more firms in a market
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A firm considers the action of others in the market
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Game theory – strategic decision making
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Oligopoly must have some market power to influence the price
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Competitive market – a firm has no influence over the market price
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Monopoly - one firm the market
2. Payoff interdependency – optimal choice by firm depends on actions of others
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Cournot Game
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1. Cournot Game
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Remember, both firms produce q 1 + q 2
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If Firm 2 sets his production level at q 2, then Firm 1 sets his production level to q 1
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Maximize profits
2. Problem 1
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Inverse demand function, P(Q) = 50 – 2Q, where Q = q 1 + q 2
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Cost functions for each firm, C(q i) = 2 q i
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Cournot Competitors
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Find best-response functions
3. We can generalize the case with N firms in the market
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Inverse demand function, P(Q) = 50 – 2Q, where Q = N q i
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The market has N firms and each firm is identical and produces q i units
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Cost functions for each firm, C(q i) = 2 q i
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Trick
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Substitute the Quantity, Q into the inverse demand function
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P(Q) = 50 – 2Nq i
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Re-write equation as, P(Q) = 50 – 2(N – 1)q i – 2q i
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Remember, all firms are identical, so q i = q j
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Substitute the q j firms into the equation
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P(Q) = 50 – 2(N – 1)q j – 2q i
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If we did not do this trick, the answer would be the N firms act like a monopoly
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Firm i's profit is:
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Remember, Firm i and Firm j are identical. Firm j would have an identical reaction function
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Substitute q j = q i into Firm i's reaction function, and solve for the quantity that Firm i will produce
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Stackelberg Model
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1. Stackelberg Model - a price leader moves first
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Stackelberg was an economist
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U.S. law makes collusion illegal
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Stackelberg Model - a price leader sets his prices first and sets high prices
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Other firms follow suit and sets high prices
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If firms compete, they drive their profits to zero
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Successful examples: General Motors, Intel
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Unsuccessful examples: American Airlines
2. Example
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Price leader earns greater profits than other firms
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Price leader has no profit function
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Steps to solve Stackelberg Model
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Problem #3
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Step 1 - calculate Airbus's reaction function
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Lerner Index
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1. Refer to Lecture 3, since derivation is very similar
2. Market share is defined as s i = q i / Q
3. Duopoly has less market share than a monopoly
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Monopoly is s i = 1
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Duopoly is 0 < s i < 1
4. If more firms enter the market, then s i becomes smaller
5. Monopoly profits are higher than a Cournot
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Two firms could collude to create a “monopoly”
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If the firms are identical, then firms split the profits 50/50
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Both firms have to limit their production using quotas
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Incentive for cheating
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One firm could cheat, and sell and produce a little more
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Both firms end up cheating on the quotas
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Collusive agreements are not a Nash equilibrium
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Bertrand Game
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1. Bertrand – Cournot game is wrong, because firms compete with prices and not quantities
2. Change assumptions
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Firms have fixed costs, f
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The rule P 1 = P 2 = MC is MR = MC, and thus does not include fixed costs
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Eventually, one firm must leave the market because profits are negative, because of fixed costs
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A monopoly market forms
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Firms have different marginal costs, such as c 2 > c 1
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Firm 1 can lower its price below Firm 2’s marginal cost
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Eventually Firm 2 has to leave the market
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Firm 1 becomes a monopoly
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Kinked Demand Function
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1. Kinked demand curve - some economists debate the existence
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