Eaton Micro 6e Ch16

7/27/2019 Eaton Micro 6e Ch16

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2005 Pearson Education Canada Inc .16.1

Chapter 16

Game Theory and Oligopoly


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Figure 16.1 The monopoly equilibrium


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Duopoly as a Prisoners Dilemma

A Duopoly is an oligopoly in whichthere are only two firms in theindustry.


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Table 16.1 Duopoly profit matrix


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From Table 16.1

L is the dominant strategy for theboth the First and the Second FirmThus the Nash-equilibriumcombination is (L,L) in which bothfirms produce 20 units and have aprofit of $200.

Yet, if they could agree to restricttheir individual outputs to 15 unitsapiece, each could earn $450.


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The Cournot Duopoly Model

Central features of the Cournot Model:1. Each firm chooses a quantity of output

instead of a price.2. In choosing an output, each firm takes

its rivals output as given.


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Figure 16.2 Finding a Cournotbest-response function


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From Figure 16.2

The First firms best responsefunction is: y 1 *=30 y 2 /2The Second firms best responsefunction is y 2 *=30 y 1 /2Taken together, these two bestresponse functions can be used tofind the equilibrium strategy combination for Cournots model.


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The Cournot Model: Key Assumptions

The profit of one firm decreases as theoutput of the other firm increases (other things equal).The Nash equilibrium output for each firmis positive.


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Isoprofit Curves

All strategy combinations that givethe first firm the chosen level of profits is known as an indifferencecurve or iosprofit curve.Profits are constant along theisoprofit curve.


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Figure 16.4 Title


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From Figure 16.4

y 1* maximizes profits for the first firmgiven the second firms output of y 2*.Any strategy combinations below theindifference curve gives the first firmmore profit than the Nash equilibrium.The result above relates to the key

assumption that the first firms profitincreases as the second firms outputdecreases.


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Figure 16.5 Joint profit notmaximized in Nash equilibrium


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Cournots Model: Conclusions

In the Nash equilibrium of thisgeneral version of the Cournotmodel, firms fail to maximize their

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


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The Cournot Model with Many Firms

With only one firm in the market, theCournot-Nash equilibrium is the monopolyequilibrium.

As the number of firms increases, outputincreases. As a result, price and aggregateoligopoly profits decrease.When there are infinitely many firms, theCournot model is, in effect, the perfectlycompetitive model.


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The Bertrand Model

The Bertrand model substitutesprices for quantities as the variablesto be chosen.The goal is to find the Nash (theBertrand-Nash) equilibrium strategycombination when firms chooseprices instead of quantities.


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The Bertrand Model: Firms BestResponse Function

Funding the best response function entailsanswering the question: Given p 2 , what valueof p 1 maximizes the first firms profit.

Four possibilities exist:1. If its rival charges a price greater than the

monopoly price (MP), the first firms bestresponse is to charge a lower price (than MP)so it can capture the entire market.


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2. If its rival charges a price less than the perunit cost of production (p 2), the first firmsbest response is to choose any price greater

than this because firm one will attract nobusiness and incur a zero profit. This outcomeis superior to matching or undercutting p 2 ,and posting losses.


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3 . If the second firms price is greater than theper unit cost of production and less than themonopoly price. (see Figure 16.6)


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Figure 16.6 Finding a Bertrandbest-response function


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4 . Suppose the second firm sets its price exactlyequal to the per unit costs.Then if the first firm sets a lower price it willincur a loss on every unit it sells and profitswill be negative. If the first firm sets a priceabove the per unit it will sell no units andprofits are zero. If the first firm sets priceequal to the per unit costs, it breaks even .


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The Bertrand-Nash Equilibrium

The Bertrand-Nash equilibrium strategycombination is the second firm and the firstfirm charging a price equal to the per unit

cost of production.At this equilibrium, each firms profit isexactly zero.


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The Limited-Output Model

In the long run, the number of firms(market structure ) is endogenous.The number of firms is an industry isdetermined by economic considerations.The key process in determining the long-run equilibrium is the possibility of entry.


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Barriers to Entry

A natural barrier to entry is setup costs.Assume all firms incur setup costs of $S

In any period, the rate of interest (i)determines the set up cost (K):K=iSAdding fixed costs to variable costs (40y)gives total cost function:

C(y)=K+40Y


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Figure16.7 The inducement to entry


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Inducement to Entry

The entrants best response functionis: y E*=30-y/2The entrants residual demandfunction is: P e =(100-y)-y e The price that will prevail if theentrant produces y e * units is:Pe *=70-y/2Profit per unit is: P e * - 40=30-y/2


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Inducement to Entry

The inducement to entry, y e * times (p e *-40) is then (30-y/) 2 .This expression gives the revenue overvariable costs that the entrant would earnif established firms continued to producey units after entry.Entry will occur if inducement to enterexceeds K


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Inducement to Entry

Entry will not occur if the output of established firms is greater than orequal to the limit output (y L)The limit price (p L ) is the priceassociated with the limit output.In this example:p L=100-y L or p L = 40+2K 1/2


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Refinements of Limited Output

How large must the fixed cost K be sothat a third firm will not enter?The generalized no-entry condition forthe Cournot models is then:

[60/(n=2) 2 ]K


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Figure 16.9 Cournot oligopolyand entry equilibrium


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Barriers to entry

The more aggressive/lesscooperative is oligopoly behaviourupon entry, the more effective setup

costs are as a barrier.Any firms decision to incur the setupcost is a strategic decision because itaffects the incentives of other firms.


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2005 P Ed ti C d I16 38

Positioning and Reacting

Positioning is concerned with actiontaken by existing firms prior toentry.Reacting refers to actions of established firms subsequent toentry.

Eaton Micro 6e Ch16

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