oligopoly and strategic interactions

Oligopoly and Strategic Interactions

Dr. Sanja Samirana PattnayakIIMT

Oligopoly

In market structures considered so far –monopolies and perfect competition- optimal strategies do not depend on the actions of the others.

Characteristics of these markets include:

Few firms High barriers to entryAbove normal profit (not necessarily though)Product differentiation may or may not exist

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Herfindahl-Hirschman Index (HHI)

An oligopoly is a market in which a few firms(usually more than 2 and less than 10) havemarket power- the power to control the price.

Economists use concentration ratios to measurethe degree to which a market or industry isoligopolistic.

The more concentrated the market/industry, theless competitive it is.

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An important measure of market concentration is the Herfindahl-Hirschman Index (HHI).

It is calculated by squaring the market share of each firm in the market and then summing the resulting numbers.

Example, consider a market with 2 firms, one with 60% market share and second with 40% share. The HHI for the market is 5200.

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In contrast a market with 10 firms, each with 10% market share, the HHI is 1000.

The Herfindahl Index helps differentiate between one industry in which four players have equal shares and another where one player has 70 per cent share and three others 10 per cent each.

The former, which is more competitive, would have a lower Herfindahl Index.

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In an extremely competitive market, say, withten players having 10 per cent share each, theindex would be 1,000.

A 1,000-2,000 value generally indicates intensecompetition. In India, values less than 2,000 isseen in the consumer electronics market.

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Oligopoly

Examples of Oligopoly markets include:Automobiles, steel, petrochemicals, electricalequipment, computers etc.

Management challenges: Strategic actions andRival behavior.

Within the managerial decision makingframework, the key trait of oligopolies isinterdependence of market players. Managerscontrol their actions, but not directly those ofothers. 7

Oligopoly

A prudent manager would take actions to affect rivals’ actions to her advantage.

Example: What are the possible rival responses to a 10% price cut by Maruti, or supplying twice of oil barrels by Iraq?

What can you do to let your rivals behave to your favour?

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Oligopoly

In oligopolistic markets, many behavioural assumptions are feasible; hence several solutions exist, with each solution based on different behavioural assumptions.

Differentiated products or notStrategic variable varyOrder of movementInformation structureCompetition one shot or repeated

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Cournot’s Quantity Competition

What would happen if firms compete by quantity?

The behavioural assumption is that manager of each firm maximizes his/her profits based on the belief that the quantity produced by her rival is invariant (fixed) with respect to his/her own quantity decisions.

Clearly, this is an interactive strategy game – now played out in strategies of plant capacity or in quantities.

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The Model

Oligopoly model in which firms produce ahomogeneous good

Each firm treats the output of its competitors as fixed, All firms decide simultaneously how much to

produce. The firms will have game plan – called “reaction

function or best response”Firm will adjust its output based on what it thinks the

other firm will produceOften called quantity competition – for example

international oil production.

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Equilibrium Concept –Nash equilibrium

Equilibrium concept: “Nash Equilibrium” . Each firm is doing the best it can given its belief on what its competitors are doing. (Details later part of the lecture on Game Theory)

Firms do the best they can and have no incentive to change their output or price, assuming all firms are taking rivals’ decisions into account.

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Cournot model: Example

An Example of the Cournot EquilibriumTwo firms face linear market demand curve

Market demand is P = 30 - Q Q is total production of both firms: Q = Q1 + Q2 Both firms have MC1 = MC2 = 0

Each Firm’s action is to choose a level of production

Firm i’s profit is

QQQQQ ijijii 30,

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Duopoly Example

We want to calculate what each firm’s profit maximizing output level, i.e. Their best response, to the other firms output decision.

This is called the firm’s reaction function

Firm 1’s Reaction Curve MR(Q2)=MC

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Duopoly Example

Calculating the reaction functions

215

CurveReaction s2' Firm

215

CurveReaction s1' Firm

0

230

12

21

11

21111

QQ

QQ

MCMR

QQQRMR

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Duopoly Example

In a Nash equilibrium Q1 and Q2 are best responses to each other.

each $100 are profits ,1030

20

102

1515*

215* and

215*

*

2

*

21

*

12

*

21

1

*1

QP

QQQ

Q

QQ

QQ

Q

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Duopoly ExampleQ1

Q2

Firm 2’s

Reaction Curve

30

15

Firm 1’s

Reaction Curve

15

30

10

10

Cournot Equilibrium

The demand curve is P = 30 - Q and

both firms have 0 marginal cost.

Comparing Oligopoly Models

Assume we have no anti-trust laws, so rival firms can talk to one another.

If managers recognize their mutual interdependence, they should agree to act in unison to maximize their joint payoff behaving as a single entity.

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Let the market demand curve is given by the inverse demand function; P=1,000-Q

The associated MR = 1,000-2Q; this MR function assumes that firms act as a single profit maximizing firm, which what collusion all about.

The cost function of each firm is identical and given by Ci(Qi)=4Qi, so MC of each firm is 4.

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Comparing Oligopoly Models We will now see how outputs, prices and profits vary according

to the type of the oligopolistic interdependence that exists in the market.

Cournot: Q1=Q2=332. Total output Q=Q1+Q2=664 and price is $336 and profits of $110,224

Bertrand: use price equal to MC. Therefore, with the given inverse demand function and cost function, P=$4and profits are zero for each firm. Total market output is 996 units. Given the symmetric firms, each firm gets half of the market.

Collusion: Q=498, P=$502 and each firm earns a profit of $124,002

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Rankings of the market output: Bertrand>Cournot>Collusive

Ranking of total profit: Collusive>Cournot>Bertrand

Ranking of Price: Collusive>Cournot>Bertrand Exercise: Find Stackelberg optimal strategy and

compare with the above model If you become a manger in an oligopolistic market, it is

important to recognize that your optimal decisions and profits will vary depending on the type of oligopolistic interactions that exists in the market.

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Price Competition-Bertrand Model

You might object to the Cournot model on the grounds that ‘in reality firms’ chose prices rather than quantities

So competition in an oligopolistic industry may occur with price instead of output.

The Bertrand Model : Firms produce a homogeneous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge?

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Price Competition – Bertrand Model

Assumptions

Homogenous goodMarket demand is P = 30 - Q where Q = Q1 + Q2MC1 = MC2 = $3

Can show the Cournot equilibrium if Q1 = Q2 = 9 and market price is $12 giving each firm a profits of $81.

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Assume here that the firms compete with price, not quantity.

Since good is homogeneous, consumers will buy from lowest price seller.

If firms charge different prices, consumers buy from lowest priced firm only.

If firms charge same price, consumers are indifferent who they buy from.

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Nash equilibrium is competitive output since firms have incentive to cut prices

Both firms set price equal to MCP = MC; P1 = P2 = $3Q = 27; Q1 & Q2 = 13.5

Both firms earn zero profit Why not charge a different price?

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Price Competition – Differentiated Products

Market shares are now determined not just by prices, but by differences in the design, performance, and durability of each firm’s product.

In these markets, more likely to compete using price instead of quantity

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ExampleDuopoly with costs of $20 Firms face the following demand curves

Firm 1’s demand: Q1 = 12 - 2P1 + P2 Firm 2’s demand: Q2 = 12 - 2P + P1

Quantity that each firm can sell decreases when it raises its own price but increases when its competitor charges a higher price

2

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Firms set prices at the same time

202-12

20)212(

20$ :1 Firm

21

2

11

211

111

PPPP

PPP

QP

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12 is firmeach for Profits

4,4, is mEquilibriuNash

413

curvereaction s2' Firm

413

curvereaction s1' Firm

0412

price maximizingprofit s'1 Firm

*

2

*

1

12

21

2111

PP

PP

PP

PPP

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Competition Versus Collusion: The Prisoners’ Dilemma

Nash equilibrium is a non-cooperativeequilibrium: each firm makes decision that gives greatest profit, given actions of competitors

Although collusion is illegal, why don’t firms cooperate without explicitly colluding?Why not set profit maximizing collusion price

and hope others follow?

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Competitor is not likely to follow

Competitor can do better by choosing a lower price, even if they know you will set the collusive level price.

We can use example from before to better understand the firms’ choices

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Possible Pricing Outcomes:

4$204)6)(2(12)6(

20

20$206)4)(2(12)4(

20

4$ 6$

$16 6$ :2 Firm 6$ :1 Firm

111

222

QP

QP

PP

PP

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Payoff Matrix for Pricing GameFirm 2

Firm 1

Charge $4 Charge $6

Charge $4

Charge $6

$12, $12 $20, $4

$16, $16$4, $20

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Competition Versus Collusion:The Prisoners’ Dilemma

We can now answer the question of why firm does not choose cooperative price.

Cooperating means both firms charging $6 instead of $4 and earning $16 instead of $12

Each firm always makes more money by charging $4, no matter what its competitor does

Unless enforceable agreement to charge $6, will be better off charging $4

Quantity Leadership: Stackelberg Model

Suppose there are two firms in the market (duopoly)

One firm (Firm1) choose a level of output before the other firm (Firm 2)

After observing the decision of Firm 1, Firm 2 decides a level of output

This model is used to describe industries in which there is a dominant firm or natural leader called the Stackelberg leader

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Suppose firm 1 is the leader and that it chooses to produce a quantity Q1

Firm 2 responds by choosing quantity Q2

Each firm knows that the equilibrium price in the market depends on the total output produced

What output should the leader choose to maximize its profits?

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Quantity Leadership: Stackelberg Model The answer depends on how the leader thinks

that the follower will react to its choice.

The leader should expect that the follower will attempt to maximize profits as well, given a choice made by the Him (leader)

Therefore, the leader should consider the follower’s profit-maximization problem in order to make a sensible decision about its own production.

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Start by the end of the game (backward): evaluate the follower’s maximization problem, taking as predetermined level of output chosen by the leader:

The follower chooses Q2 such that Π2 (Q1, Q2) is maximized

You will find Q2 = f(Q1), the reaction function for the follower

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Quantity Leadership: Stackelberg Model Solve the leader’s optimization problem, subject to

the reaction of the follower

The leader chooses Q1 such Π1 (Q1, Q2) is maximized subject to Q2 = f(Q1), i.e., max Π1 (Q1, f(Q1))

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Cournot and Stackelberg models are alternative representations of oligopolistic behavior.

Which model is more appropriate depends on the industry.

For an industry roughly comprising of similar firms (none having strong operating advantage or leadership position), the Cournot model is the most appropriate one.

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On the other hand, industry dominated by a large firm that usually takes the lead in introducing new product or setting price.

The mainframe computer market is an example, with IBM the leader.

Then the Stackelberg model may be more realistic.

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oligopoly and strategic interactions

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