© 2005 pearson education canada inc. 16.1 chapter 16 game theory and oligopoly

© 2005 Pearson Education Canada Inc.16.1

Chapter 16Chapter 16

Game Theory and OligopolyGame Theory and Oligopoly


Figure 16.1 The monopoly equilibriumFigure 16.1 The monopoly equilibrium


Duopoly as a Prisoner’s DilemmaDuopoly as a Prisoner’s Dilemma

A Duopoly is an oligopoly in which A Duopoly is an oligopoly in which there are only two firms in the there are only two firms in the industry.industry.


Table 16.1 Duopoly profit matrixTable 16.1 Duopoly profit matrix


From Table 16.1From Table 16.1

L is the dominant strategy for the L is the dominant strategy for the both the First and the Second Firmboth the First and the Second Firm

Thus the Nash-equilibrium Thus the Nash-equilibrium combination is (L,L) in which both combination is (L,L) in which both firms produce 20 units and have a firms produce 20 units and have a profit of $200.profit of $200.

Yet, if they could agree to restrict Yet, if they could agree to restrict their individual outputs to 15 units their individual outputs to 15 units apiece, each could earn $450.apiece, each could earn $450.


The Oligopoly ProblemThe Oligopoly Problem

Oligopolists have a clear incentive to Oligopolists have a clear incentive to collude or cooperate.collude or cooperate.

Oligopolists have a clear incentive to Oligopolists have a clear incentive to cheat on any simple collusive or cheat on any simple collusive or cooperative agreement.cooperative agreement.

If an agreement is not a Nash If an agreement is not a Nash equilibrium, it is not self-enforcing.equilibrium, it is not self-enforcing.


The Cournot Duopoly ModelThe Cournot Duopoly Model

Central features of the Cournot Model:Central features of the Cournot Model:

1.1. Each firm chooses a quantity of output Each firm chooses a quantity of output instead of a price.instead of a price.

2.2. In choosing an output, each firm takes In choosing an output, each firm takes its rival’s output as given.its rival’s output as given.


Figure 16.2 Finding a Cournot Figure 16.2 Finding a Cournot best-response functionbest-response function


From Figure 16.2 From Figure 16.2

The First firm’s best response The First firm’s best response function is: yfunction is: y11

**=30 – y=30 – y22/2/2 The Second firm’s best response The Second firm’s best response

function is yfunction is y22**=30 – y=30 – y11/2 /2

Taken together, these two best Taken together, these two best response functions can be used to response functions can be used to find the find the equilibrium strategy equilibrium strategy combination combination for Cournot’s model. for Cournot’s model.


Figure 16.3 The Cournot equilibriumFigure 16.3 The Cournot equilibrium


The Cournot Model: Key AssumptionsThe Cournot Model: Key Assumptions

The profit of one firm decreases as the The profit of one firm decreases as the output of the other firm increases (other output of the other firm increases (other things equal).things equal).

The Nash equilibrium output for each firm The Nash equilibrium output for each firm is positive.is positive.


Isoprofit CurvesIsoprofit Curves

All strategy combinations that give All strategy combinations that give the first firm the chosen level of the first firm the chosen level of profits is known as an indifference profits is known as an indifference curve or iosprofit curve. curve or iosprofit curve.

Profits are constant along the Profits are constant along the isoprofit curve.isoprofit curve.


Figure 16.4 TitleFigure 16.4 Title


From Figure 16.4From Figure 16.4

yy11* maximizes profits for the first firm * maximizes profits for the first firm given the second firm’s output of ygiven the second firm’s output of y22*.*.

Any strategy combinations below the Any strategy combinations below the indifference curve gives the first firm indifference curve gives the first firm more profit than the Nash equilibrium.more profit than the Nash equilibrium.

The result above relates to the key The result above relates to the key assumption that the first firm’s profit assumption that the first firm’s profit increases as the second firm’s output increases as the second firm’s output decreases.decreases.


Figure 16.5 Joint profit not Figure 16.5 Joint profit not maximized in Nash equilibriummaximized in Nash equilibrium


Cournot’s Model: ConclusionsCournot’s Model: Conclusions

In the Nash equilibrium of this In the Nash equilibrium of this general version of the Cournot general version of the Cournot model, firms fail to maximize their model, firms fail to maximize their joint profit.joint profit.

Relative to joint profit maximization, Relative to joint profit maximization, firms produce too much output in the firms produce too much output in the Nash equilibrium.Nash equilibrium.


The Cournot Model with Many FirmsThe Cournot Model with Many Firms

With only one firm in the market, the With only one firm in the market, the Cournot-Nash equilibrium is the monopoly Cournot-Nash equilibrium is the monopoly equilibrium. equilibrium.

As the number of firms increases, output As the number of firms increases, output increases. As a result, price and aggregate increases. As a result, price and aggregate oligopoly profits decrease.oligopoly profits decrease.

When there are infinitely many firms, the When there are infinitely many firms, the Cournot model is, in effect, the perfectly Cournot model is, in effect, the perfectly competitive model.competitive model.


The Bertrand ModelThe Bertrand Model

The The Bertrand modelBertrand model substitutes substitutes prices for quantities as the variables prices for quantities as the variables to be chosen.to be chosen.

The goal is to find the Nash (the The goal is to find the Nash (the Bertrand-Nash) equilibrium strategy Bertrand-Nash) equilibrium strategy combination when firms choose combination when firms choose prices instead of quantities.prices instead of quantities.


The Bertrand Model: Firm’s Best The Bertrand Model: Firm’s Best Response FunctionResponse Function

Funding the best response function entails Funding the best response function entails answering the question: Given panswering the question: Given p22, what value , what value of pof p11 maximizes the first firm’s profit. maximizes the first firm’s profit.

Four possibilities exist:Four possibilities exist:

1.1. If its rival charges a price greater than the If its rival charges a price greater than the monopoly price (MP), the first firm’s best monopoly price (MP), the first firm’s best response is to charge a lower price (than MP) response is to charge a lower price (than MP) so it can capture the entire market. so it can capture the entire market.



2.2. If its rival charges a price less than the per If its rival charges a price less than the per unit cost of production (punit cost of production (p22), the first firm’s ), the first firm’s best response is to choose any price greater best response is to choose any price greater than this because firm one will attract no than this because firm one will attract no business and incur a zero profit. This outcome business and incur a zero profit. This outcome is superior to matching or undercutting pis superior to matching or undercutting p22, , and posting losses.and posting losses.



33. . If the second firm’s price is greater than the If the second firm’s price is greater than the per unit cost of production and less than the per unit cost of production and less than the monopoly price. (see Figure 16.6)monopoly price. (see Figure 16.6)


Figure 16.6 Finding a Bertrand Figure 16.6 Finding a Bertrand best-response functionbest-response function



44. . Suppose the second firm sets its price exactly Suppose the second firm sets its price exactly equal to the per unit costs.equal to the per unit costs.

Then if the first firm sets a lower price it will Then if the first firm sets a lower price it will incur a loss on every unit it sells and profits incur a loss on every unit it sells and profits will be negative. If the first firm sets a price will be negative. If the first firm sets a price above the per unit it will sell no units and above the per unit it will sell no units and profits are zero. If the first firm sets price profits are zero. If the first firm sets price equal to the per unit costs, it breaks evenequal to the per unit costs, it breaks even..


The Bertrand-Nash EquilibriumThe Bertrand-Nash Equilibrium

The Bertrand-Nash equilibrium strategy The Bertrand-Nash equilibrium strategy combination is the second firm and the first combination is the second firm and the first firm charging a price equal to the per unit cost firm charging a price equal to the per unit cost of production.of production.

At this equilibrium, each firm’s profit is exactly At this equilibrium, each firm’s profit is exactly zero.zero.


The Limited-Output ModelThe Limited-Output Model

In the long run, the number of firms In the long run, the number of firms (market structure ) is (market structure ) is endogenous.endogenous.

The number of firms is an industry is The number of firms is an industry is determined by economic considerations.determined by economic considerations.

The key process in determining the long-The key process in determining the long-run equilibrium is the run equilibrium is the possibility of entry.possibility of entry.


Barriers to EntryBarriers to Entry

A natural barrier to entry is A natural barrier to entry is setup costs. setup costs. Assume all firms incur setup costs of $SAssume all firms incur setup costs of $S In any period, the rate of interest (i) In any period, the rate of interest (i)

determines the set up cost (K):K=iSdetermines the set up cost (K):K=iS Adding fixed costs to variable costs (40y) Adding fixed costs to variable costs (40y)

gives total cost function: gives total cost function:

C(y)=K+40YC(y)=K+40Y


Inducement to EntryInducement to Entry

If the fixed costs (K) is a barrier to If the fixed costs (K) is a barrier to entry, what is an inducement to entry, what is an inducement to entry?entry?

An inducement to entry is the excess An inducement to entry is the excess of revenue over variable costs. of revenue over variable costs.


Figure16.7 The inducement to entryFigure16.7 The inducement to entry


Inducement to Entry Inducement to Entry

The entrant’s best response function The entrant’s best response function is: yis: yEE

**=30-y/2=30-y/2 The entrant’s residual demand The entrant’s residual demand

function is: Pfunction is: Pee=(100-y)-y=(100-y)-yee

The price that will prevail if the The price that will prevail if the entrant produces yentrant produces yee* units is: P* units is: Pee*=70-*=70-y/2y/2

Profit per unit is: PProfit per unit is: Pee* - 40=30-y/2* - 40=30-y/2



The inducement to entry, yThe inducement to entry, yee* times (p* times (pee*-*-40) is then (30-y/)40) is then (30-y/)22..

This expression gives the revenue over This expression gives the revenue over variable costs that the entrant would earn variable costs that the entrant would earn if established firms continued to produce if established firms continued to produce y units after entry.y units after entry.

Entry will occur if inducement to enter Entry will occur if inducement to enter exceeds Kexceeds K



Call the smallest value of y such that no Call the smallest value of y such that no entry occurs the entry occurs the limit output (ylimit output (yLL).).

(30-y(30-yLL/2)/2)22=K=K

Solving for YSolving for YLL: Y: YLL= 60-2K= 60-2K1/21/2

If K=$100, YIf K=$100, YLL=40 units, If K=$225, Y=40 units, If K=$225, YLL=30 =30 units, etc. (see Figure 16.8)units, etc. (see Figure 16.8)



Entry will not occur if the output of Entry will not occur if the output of established firms is greater than or established firms is greater than or equal to the limit output (yequal to the limit output (yLL))

The The limit price (plimit price (pLL)) is the price is the price associated with the limit output.associated with the limit output.

In this example:In this example:

ppLL=100-y=100-yLL or p or pLL = 40+2K = 40+2K1/21/2


Figure 16.8 Identifying the limit Figure 16.8 Identifying the limit price and the limit outputprice and the limit output


Refinements of Limited OutputRefinements of Limited Output

How large must the fixed cost K be so How large must the fixed cost K be so that a third firm will not enter?that a third firm will not enter?

The generalized no-entry condition for the The generalized no-entry condition for the Cournot models is then:Cournot models is then:

[60/(n=2)[60/(n=2)22]≤K]≤K


Figure 16.9 Cournot oligopoly Figure 16.9 Cournot oligopoly and entry equilibriumand entry equilibrium


Barriers to entryBarriers to entry

Development cost K is a barrier to Development cost K is a barrier to entry, as it differentiates established entry, as it differentiates established firms and new potential entrants.firms and new potential entrants.

The manner in which this The manner in which this differentiation affects the differentiation affects the inducement to enter (profits) inducement to enter (profits) depends upon the nature of the depends upon the nature of the oligopoly behaviour upon entry.oligopoly behaviour upon entry.


Barriers to entryBarriers to entry

The more aggressive/less The more aggressive/less cooperative is oligopoly behaviour cooperative is oligopoly behaviour upon entry, the more effective setup upon entry, the more effective setup costs are as a barrier.costs are as a barrier.

Any firm’s decision to incur the setup Any firm’s decision to incur the setup cost is a strategic decision because it cost is a strategic decision because it affects the incentives of other firms.affects the incentives of other firms.


Positioning and ReactingPositioning and Reacting

PositioningPositioning is concerned with action is concerned with action taken by existing firms prior to entry.taken by existing firms prior to entry.

ReactingReacting refers to actions of refers to actions of established firms subsequent to established firms subsequent to entry.entry.

© 2005 pearson education canada inc. 16.1 chapter 16 game theory and oligopoly

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