


Oligopolies and Game Theory
Lecture 5


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

Cournot Game 
1. Cournot Game
Remember, both firms produce q_{1} + q_{2}
If Firm 2 sets his production level at q_{2}, then Firm 1 sets his production level to q_{1}
Maximize profits
Solve
for q_{1} = R_{1}(q_{2})
Solve
for q_{2} = R_{2}(q_{2})
Remember
has both q_{1} and q_{2}
has both q_{1} and q_{2}
Use algebra to solve two equations for two unknowns
2. Problem 1
Inverse demand function, P(Q) = 50 – 2Q, where Q = q_{1} + q_{2}
Cost functions for each firm, C(q_{i}) = 2 q_{i}
Cournot Competitors
Find bestresponse functions
3. We can generalize the case with N firms in the market
Inverse demand function, P(Q) = 50 – 2Q, where Q = N q_{i}
The market has N firms and each firm is identical and produces q_{i} units
Cost functions for each firm, C(q_{i}) = 2 q_{i}
Trick
Substitute the Quantity, Q into the inverse demand function
P(Q) = 50 – 2Nq_{i}
Rewrite equation as, P(Q) = 50 – 2(N – 1)q_{i} – 2q_{i}
Remember, all firms are identical, so q_{i} = q_{j}
Substitute the q_{j} firms into the equation
P(Q) = 50 – 2(N – 1)q_{j} – 2q_{i}
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 q_{j} = q_{i} into Firm i's reaction function, and solve for the quantity that Firm i will produce

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

Lerner Index 
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
Monopoly is s_{i} = 1
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
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

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 P_{1} = P_{2} = 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 c_{2} > c_{1}
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

Kinked Demand Function 
1. Kinked demand curve  some economists debate the existence


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