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Oligopolies and Game Theory
Lecture 5
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Oligopolies |
1. Market Stucture and Game Theory
Oligopolies – two or more firms in a market
A firm considers the action of others in the market
Game theory – strategic decision making
Oligopoly must have some market power to influence the price
Competitive market – a firm has no influence over the market price
Monopoly - one firm the market
2. Payoff interdependency – optimal choice by firm depends on actions of others
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Cournot Game |
1. Cournot Game



Remember, both firms produce q1 + q2
If Firm 2 sets his production level at q2, then Firm 1 sets his production level to q1
Maximize profits



2. Problem 1
Inverse demand function, P(Q) = 50 – 2Q, where Q = q1 + q2
Cost functions for each firm, C(qi) = 2 qi
Cournot Competitors
Find best-response functions




3. We can generalize the case with N firms in the market
Inverse demand function, P(Q) = 50 – 2Q, where Q = N qi
The market has N firms and each firm is identical and produces qi units
Cost functions for each firm, C(qi) = 2 qi
Trick
Substitute the Quantity, Q into the inverse demand function
P(Q) = 50 – 2Nqi
Re-write equation as, P(Q) = 50 – 2(N – 1)qi – 2qi
Remember, all firms are identical, so qi = qj
Substitute the qj firms into the equation
P(Q) = 50 – 2(N – 1)qj – 2qi
If we did not do this trick, the answer would be the N firms act like a monopoly
Firm i's profit is:


Remember, Firm i and Firm j are identical. Firm j would have an identical reaction function
Substitute qj = qi into Firm i's reaction function, and solve for the quantity that Firm i will produce

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Stackelberg Model |
1. Stackelberg Model - a price leader moves first
Stackelberg was an economist
U.S. law makes collusion illegal
Stackelberg Model - a price leader sets his prices first and sets high prices
Other firms follow suit and sets high prices
If firms compete, they drive their profits to zero
Successful examples: General Motors, Intel
Unsuccessful examples: American Airlines
2. Example
Price leader earns greater profits than other firms
Price leader has no profit function
Steps to solve Stackelberg Model
Problem #3
Step 1 - calculate Airbus's reaction function




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Lerner Index |
1. Refer to Lecture 3, since derivation is very similar

2. Market share is defined as si = qi / Q
3. Duopoly has less market share than a monopoly
Monopoly is si = 1
Duopoly is 0 < si < 1
4. If more firms enter the market, then si becomes smaller
5. Monopoly profits are higher than a Cournot
Two firms could collude to create a “monopoly”
If the firms are identical, then firms split the profits 50/50
Both firms have to limit their production using quotas
Incentive for cheating
One firm could cheat, and sell and produce a little more
Both firms end up cheating on the quotas
Collusive agreements are not a Nash equilibrium
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Bertrand Game |
1. Bertrand – Cournot game is wrong, because firms compete with prices and not quantities

2. Change assumptions
Firms have fixed costs, f
The rule P1 = P2 = MC is MR = MC, and thus does not include fixed costs
Eventually, one firm must leave the market because profits are negative, because of fixed costs
A monopoly market forms
Firms have different marginal costs, such as c2 > c1
Firm 1 can lower its price below Firm 2’s marginal cost
Eventually Firm 2 has to leave the market
Firm 1 becomes a monopoly
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Kinked Demand Function |
1. Kinked demand curve - some economists debate the existence


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