Chapter 14: Oligopoly & Game Theory

Introduction

• We have looked at two ends of the spectrum:– Very competitive markets (perfect competition)– Very uncompetitive markets (monopoly)

• Now we are going to look somewhere in the middle (Oligopoly)

• We’ll look at firm’s with some market power (like a monopolist), but with strong competitors (like perfect competition)

Oligopoly• Oligopoly refers to a market with a small

number of firms (2, 3, 4, 5) whose behavior is interdependent

• Interdependent means that Firm A’s choices effect Firm B

• For example: Subway’s ad campaign (“Eat Fresh”) certainly impacts the demand for Subway, but it will also affect the demand for Quiznos, McDonald’s, Burger King, etc.)

• The price Pepsi charges effects not only their sales, but also Coke’s sales

Types of Oligopoly• There are a variety of different types of oligopoly• In oligopoly, the firms can make identical

(homogeneous) products or differentiated products

• How can products be differentiated?– Physical qualities (this cereal has a better taste)– Sales locations (you can only get this online)– Services (this bank charges $2 to see a teller)– Image (advertising)

Models of Oligopoly

• Most of the widely-used models of oligopoly are too quantitative to describe here

• HOWEVER, the key element to consider is the fact that the strong interdependence among firms results in strategic behavior

• “How much should I advertise if my rival…?”• “If I cut my price, I know my rival will…”• A useful way to handle this strategic behavior

is through the use of GAME THEORY

Game Theory• Game Theory is a method we can use to

analyze the decision-making process for these strategic firms

• Each “game’” has (a) players, (b) strategies, and (c) payoffs

• Players – these will be the firms• Strategies – the choices the players have (what

price should I charge, should I enter the market)• Payoffs – what the player receives for playing

the game (profits)

Example: Prisoner’s Dilemma• Two thieves, Dave and Wes, are arrested as suspects in

a murder• The police believes they are guilty, but can’t prove it

without a confession• The two suspects are interrogated in separate rooms

and given the same speech:– “If you confess and testify against your buddy, we’ll let you go

free”– “If your buddy turns you in, we’ll ask for the maximum sentence”

• If neither confess, then there won’t be enough evidence to convict them and they’ll only go to jail for a minor offense (drug possession, underage drinking, etc.)

• If both confess, they’ll both go to jail for the crime but they won’t do the maximum

The Payoff Matrix• We will represent this game in a matrix form (like

a table)• In the matrix, we have all of the following

information:– Each player (Dave and Wes)– Each strategy available (Confess, Remain Silent)– The payoff for each possible combination (the amount

of time in jail)• We will use game theory to try and

anticipate/predict the optimal choices for both players

55

0 10

10

0

1

1

Confess

Silent

DAVE

Confess Silent

WES

Payoff Matrix

• How do we read this matrix/table?• Dave’s strategies and payoffs are represented in BLUE• Wes’ strategies and payoffs are represented in GREEN

FOR EXAMPLE:

If Dave confesses and Wes stays silent, then the payoffs are…

Dave goes free (no jail time) and Wes serves 10 years in prison

Equilibrium• Now that we understand each players’ choices

(strategies), we need to figure out what is the optimal choice for each player to make

• To help us determine the optimal strategies, we will look for the NASH EQUILIBRIUM…

Nash Equilibrium• Nash Equilibrium – The strategies or actions in

which each firm does the best it can given its’ competitors’ actions

• The key is that the Nash Equilibrium gives us the best strategy given what the other’s are doing

• This implies that you have no incentive to change your behavior because you are doing the best thing you can, given what everyone else is doing

• The explanation in the movie is wrong…

55

0 10

10

0

1

1

Confess

Silent

DAVE

Confess Silent

WES

If Dave confesses, what is Wes’ best response?

Wes goes to jail for 10 years if he stays silent, but he only goes to jail for 5 years if he confesses, too

So, “confess” is Wes’ best response

What is Dave stays silent? What is Wes’ best response now?

Wes goes to jail for a year if he stays silent, but he goes free if he confesses

So, “confess” is Wes’ best response

For either of Dave’s choices, Wes’ best response is to CONFESS

Using the same logic for Dave’s best responses, we can find the Nash Equilibrium…

55

0 10

10

0

1

1

Confess

Silent

DAVE

Confess Silent

WES

The Nash Equilibrium occurs where both people’s best responses overlap…

The Nash Equilibrium is that both players should “Confess” and receive 5 years in prison

“But Adam, couldn’t they BOTH be BETTER OFF if they both stayed SILENT?”

“Yes, they could BUT both players would have an incentive to change their strategy. If I knew you were going to stay Silent, I’d be better off Confessing (and vice versa).”

So, the NASH EQUILIBRIUM point is the only stable (sustainable) outcome

Price-Setting Game: Coke vs. Pepsi

• Let’s examine a potential situation where Coke and Pepsi simultaneously choose what price to charge

• To make this simple, suppose each firm can choose whether to charge a high price or a low price

• If they charge the same price, they split sales in the market and earn equal profit

• If one firm charges a lower price (“undercutting”), that lower price firm earns more profit than the high priced firm

$500

$500

$1000

$200

$200

$1000

$700

$700

Low Price High Price

Low Price

HighPrice

Pepsi

Coke

Pepsi’s perspective: If Coke charges the low price, Pepsi earns $500 charging the low price but only $200 by charging the high price better off by charging the low price.If Coke charges the high price, Pepsi earns $1,000 by charging the low price and $700 charging the high price earn more by charging the low price.

Coke faces the same incentives

Each seller will charge the low price, regardless of what the other does each earns $500 a day

Price-Setting Payoff Matrix

Just like the Prisoner’s dilemma, both firms would be BETTER OFF if they both charged the HIGH PRICE, but that strategy is not sustainable

Extending the Game…

• We’ve looked at just two choices up until this point (Confess/Stay Silent OR High Price/Low Price)

• The same technique for finding the Nash Equilibrium applies to situations where there are more than two moves

• Consider the following example about Coke and Pepsi choosing how much to spend on advertising

• TopHat question…

Other Examples…• The concept of a Nash Equilibrium can be

used in other situations…even when there is no payoff matrix to examine

• As an example, let’s think of two firms choosing where to build their stores

• Example: Let’s think of two coffee shops (Starbucks and Espresso Joe’s) trying to decide where along Route 96 to build their new coffee shops

• We will think of modeling Route 96 as a Line

Linear Model

• Route 96 will be modeled as a LINE• Starbucks and Espresso Joe’s must decide

where along the line to set up their shop• In the linear model, there are consumers all

along the line• Consumers purchase from the store that is

closest to them• The point, therefore, is to choose the optimal

location so that the most consumers visit your store

Linear Model

Broad St.Fortress Blvd.

How does this model work?

The consumers purchase from the store that is closest to them

For example, suppose Starbucks and Espresso Joe’s are located here…

Starbucks Espresso Joe’s

Consumers that buy from Joe’sConsumers that buy from Starbucks

Nash EquilibriumIn order to find the Nash Equilibrium, we need to determine each firm’s BEST RESPONSE (just as we did when looking at a payoff matrix)

Broad St.Fortress Blvd.

Espresso Joe’s

If Espresso Joe’s is located at the location above, where would Starbucks want to locate? Remember that they want to get the most customers as possible.

Starbucks would want to locate as close to Joe’s as possible (so that they are the closest store for all of the people out towards Fortress Blvd.)

Starbucks

Nash Equilibrium

Broad St.Fortress Blvd.

Espresso Joe’sStarbucks

The Nash Equilibrium strategy is for both firms to locate NEXT TO EACH OTHER in the middle of the line => they each get half of the customers

This choice is the only STABLE strategy (there is no incentive for either firm to “move”)

No firm can gain more customers by switching their location

Minimum Differentiation

• This idea that firms want to locate close to each other is something that we see all the time…– Gas stations are usually at an intersection with other

gas stations– One block in Charlottesville has three coffee shops

but there isn’t another one for over a mile– Coke and Pepsi make their colas almost identical

(locating close to their rival)• The Nash Equilibrium helps us determine what

the optimal strategies are, given what our rivals are going to do

Multi-period (Sequential) Games

• In multi-period games, there is a timing element– One firm chooses their price, then the other firms set

their price– Your firm is trying to decide which pricing strategy to

adopt to keep out future (potential) rivals– The Stackelberg model was an example of a

sequential game

• In the simultaneous-move game (static), we used the normal form representation

• For sequential games, we will use an extensive form representation (tree diagram)

Player 1

Player 2 Player 2

UPDOWN

UP

UP

DO

WN

DO

WN

(10, 15) (5, 5) (0, 0) (6, 20)

Solution Technique

• To solve for the Nash equilibrium strategies in sequential games, we use backward induction– We solve the game from the end to the beginning

• How? Start at the final stage of the game and figure out what the firm would do if the game was at the point

• After considering all the final choices, move up to the preceding stage of the game and figure what that firm would do knowing how the other firm would behave in the final stage of the game

Player 1

Player 2 Player 2

UPDOWN

UP

UP

DO

WN

DO

WN

(10, 15) (5, 5) (0, 0) (6, 20)

Nash Equilibrium• The Nash equilibrium in this game is for Player 1

to choose UP and then Player 2 to choose UP• Playing these strategies gives Player 1 a pay-off

of $10 and Player 2 a pay-off of $20

• Now try one on your own…• Firm A is a pharmaceutical company thinking

about developing a new cancer drug• Firm B is a generic drug manufacturer that may

(or may not) clone Firm 1’s drug

Firm A

Firm B

Introduce

DrugD

on’t

Intr

oduc

e D

rug

Clone

Don’t

Clone

(0, 0) (100, 0) (-5, 20)

Oligopoly vs. Perfect Competition

• As we did with monopoly, it is useful to measure oligopoly against perfect competition

• Unfortunately, we haven’t used equations or graphs to characterize oligopoly, so the comparison isn’t quite as easy…but we can still make some predictions based on what we do know

• Let’s look at price and profits

Oligopoly vs. Perfect Competition

• Either because (a) there are fewer firms or (b) firms often have some sort of market power, prices under oligopoly tend to be higher than perfect competition

• Higher prices also imply less less output• Because there are barriers to entry in oligopoly

which keep out potential competitors, there is the possibility of positive long run profits

• Oligopoly is usually “better” for consumers than monopoly, however

The last words on market structure and consumer

welfare…

As markets become more competitive, the consumer usually benefits through

lower prices and increased output