Remark ON THE RELATIVE PAYOFFS OF BOTH PLAYERS From the tabular array above, the university has two schemes, that is ; to offer support and non offer support. The pupil besides has two schemes, that is ; survey to go through and make non analyze to go through. The university is the row participant while the pupil is the column participant.

However, if the university chooses to offer support, she gets a Fringy Utility of 6 if the pupil chooses to analyze and the pupil gets a final payment of 4. It is the best final payment to the university sing that she has offered support and the pupil fastidiously decides to analyze. At this point, the university is fulfilled. But if the pupil chooses non to analyze, when the university chooses to offer support, the university gets a negative final payment ( -2 ) and the pupil gets a final payment of 6. The negative fringy public-service corporation to the university suggests that as a consequence of the pupil non analyzing, it impacts negatively on the university in the sense that the pupil may take to postpone, or worse still, go a dropout of the university and may even go a nuisance to the society. All of this does non portray the university in a good image. Besides, as a consequence of the pupil dropping out of school, the university ‘s outgo will increase with no equal matching addition in gross accruing to the university.

On the other manus, if the university chooses non to offer support, she gets a final payment of -2 if the pupil chooses to analyze to go through while the pupil gets a final payment of 2. In this instance, the university will be disappointed by non offering support when the pupil chooses survey to go through. The University chose non offer support organizing the belief that the pupil will take non to analyze to go through. If the University chooses non offer support and the pupil chooses non to analyze, they get a final payment of 0 each ; connoting that cipher wins or looses or regrets his class of action.

## ( B )

## Presentation THAT THERE IS NO STABLE NASH EQUILIBRIUM IN PURE STRATEGIES

Nash equilibrium can be seen as a scheme in which there is no inducement for the participants in a game to divert. This means that divergence to another scheme will non be profitable. Therefore, it can be seen as a scheme that maximises a participant ‘s final payment given the other participant ‘s scheme ( Rasmusen 2007:26-27 ) . In other words, in a nash equilibrium, it will pay a participant to keep his current scheme given that the other participant does non alter his scheme.

By pure schemes, it is meant that each participant is taking a scheme one time and for all. That is to state that the participant sticks to his pick ( Varian 2010:524-525 ) . An unstable Nash equilibrium implies that there is more than one nash equilibrium result in a game or that no 1 state of affairs is more preferred for all participants ( Emelichev etal 2003 ) . As noted by Varian 2010, holding an unstable Nash equilibrium is one of the jobs of the nash equilibrium impression

To show that there is no stable nash equilibrium in pure schemes for this game, we consider the determinations to both participants below:

## Payoff TO UNIVERSITY:

Offer support, pupil survey = 6

Not offer support, pupil survey = -2

## Offer support if pupil surveies

Offer support, pupil do non analyze = -2

Not offer support, pupil do non analyze = 0

## Not offer support if pupil does non analyze

## Payoff TO STUDENT:

Study, University offers support = 4

Do non analyze, University offers support = 6

## Do non analyze if University offers support

Study, University does non offer support = 2

Do non analyze, University does non offer support = 0

## Survey if University does non offer support.

From the above, it can be seen that there is no convergence of at least one scheme combination by both participants. If the University chooses to ‘offer support if the pupil surveies ‘ , so the pupil will non analyze. If the University chooses ‘not to offer support if the pupil does non analyze ‘ , so the pupil will take to analyze. Besides, if the pupil chooses ‘not to analyze if the University offers support ‘ , the University will non offer support. And if the pupil chooses to ‘study if University does non offer support ‘ , so the University will offer support.

Therefore, there is no stable nash equilibrium in this game.

## ( C )

## MIXED STRATEGY EQUILIBRIUM FOR BOTH PLAYERS

Assorted scheme, harmonizing to Varian ( 2010:526 ) can be seen when agents are allowed to randomise their schemes. In assorted scheme, chances are assigned to each picks and the picks are really played with the assigned chances.

The chance of a participant is gotten, taking into history the final payments of the other participant in the game.

Let the chance of the University offering support and the chance of the university non offering support be Ps and ( 1-Ps ) severally. And the chance of the pupil analyzing and non analyzing to go through be Pq and ( 1-Pq ) severally. Therefore, following the payoff-equating method noted in Rasmusen ( 2007:74 ) , the chances of the assorted scheme is calculated as follows:

## Probabilities for the University taking into history the pupil ‘s final payment:

4Ps + 2 ( 1-Ps ) = 6Ps + 0 ( 1-Ps )

Traveling like footings to one side and roll uping them,

-2Ps = -2 ( 1-Ps ) – – – – – – – – – – ( 1 )

But Ps + ( 1 – Postscript ) =1 – – – – – – – – ( 2 )

-2Ps = -2 + 2Ps

-4Ps = -2

Ps = -2/-4

## Ps = A? or 0.5

Puting Ps = 0.5 into ( 2 ) ,

0.5 + ( 1-Ps ) = 1

( 1-Ps ) = 1 – 0.5

## ( 1-Ps ) = 0.5 or A?

## Probabilities for the pupil taking into history the University ‘s final payment:

6Pq + [ -2 ( 1-Pq ) ] = -2Pq + 0 ( 1-Pq )

Traveling and roll uping like footings,

8Pq = 2 ( 1-Pq ) – – – – – – – – – – – – – ( 3 )

But Pq + ( 1-Pq ) =1 – – – – – – – – – – ( 4 )

8Pq = 2 – 2Pq

10Pq = 2

## Pq = 2/10 =1/5 or 0.2

Substituting Pq = 0.2 into ( 4 ) ,

0.2 + ( 1-Pq ) = 1

( 1-Pq ) = 1 – 0.2

## ( 1-Pq ) = 0.8

We can now find the assorted scheme equilibrium result for both participants, therefore:

university = [ 0.5 ( 0.2*6 ) + ( 0.8 *- 0.2 ) ] + 0.5 ( 0.2 * -2 ) + ( 0.8 * 0 )

=0.5 ( 1.2 – 1.6 ) + 0.5 ( -0.4 + 0 )

0.5 ( -0.4 ) + 0.5 ( -0.4 )

=-0.2 -0.2

=-0.4 ( & lt ; 0 )

pupil = [ 0.2 ( 0.5 * 4 ) + ( 0.5 * 2 ) + 0.8 ( 0.5 * 6 ) + ( 0.5 * 0 )

=0.2 ( 2 + 1 ) + 0.8 ( 3 + 0 )

=0.2 ( 3 ) + 0.8 ( 3 )

=0.6 + 2.4

=3 ( & gt ; 0 )

This means that with the usage of assorted scheme, both participants ( university and pupil ) will hold an result of-0.4 and 3 on norm severally regardless of which scheme they use. The assorted scheme Nash equilibrium which can non be ‘exploited ‘ by either participant are:

University: 0.5Ps + 0.5 ( 1-Ps ) ;

Student: 0.2Pq + 0.8 ( 1-Pq )

In drumhead, the chances of a assorted scheme are represented as:

with results

## ( D )

## CRITIQUE OF THE MIXED STRATEGY NASH EQUILIBRIUM

( I ) Mixed scheme nash equilibrium poses a job by presuming that both participants have the same result no affair what scheme they choose. The inquiry arises as to why and how participants randomize their determinations. It is intuitively debatable.

( two ) Peoples are besides unable to bring forth random results without the assistance of a random or pseudo-random generator. Players who are inexperienced with randomizing may ne’er achieve equilibrium if they are unable to engage or pay for the services of a random generator.

## Question 2

Given the parametric quantities = 359, , Ca =109 and Cb = 105

Where P =

P= The market uncluttering monetary value of the merchandise in the market

Q= The entire end product for both houses to the market

and are parametric quantities

The market reverse demand is given as:

## P = 359 – 0.10 ( qa + qb )

And Marginal cost of house a ( MCa ) = 109

Fringy cost of house B ( MCb ) = 105

General premises of the theoretical account:

( I ) The houses have homogeneous merchandises

( two ) Each house has a changeless but different fringy cost, i.e 109 and 105 for houses a and B severally.

( three ) There are two houses in the industry i.e. Firm a and house B.

## ( A )

## Net income Function FOR BOTH FIRMS.

Net income can merely be seen as the difference between the income ( gross ) of a house and its cost. Where gross or income is monetary value multiplied by measure.

The generalized net income map is given of the signifier:

Max P = ( P – I ) chi

Where p= monetary value

I = Marginal cost

chi = measure

Given P = 359 – 0.10 ( qa + qb )

the net income map for house a is:

a = ( P – aA ) qa

a = [ 359 – 0.10 ( qa + qb ) – 109 ] qa

a = 250qa – 0.10qa2 – 0.10qaqb – – – – – – – – – – – – – – – ( 1 )

The net income map for house B is:

B = ( P – B ) qb

B = [ 359 – 0.10 ( qa + qb ) – 105 ] qb

B = 254 – 0.10qb2 – 0.10qaqb – – – – – – – – – – – – – – – – – ( 2 )

## ( B )

## NASH EQUILIBRIUM OUTCOME IN PROFITS IN A COURNOT GAME

In a cournot theoretical account, no 1 manufacturer is able to find the monetary value of its merchandise entirely, because entire measure of the merchandise is determined by all the participants[ 1 ]in the game. Harmonizing to Bierman and Fernandez, ‘the market monetary value per unit of end product, P, received by all houses is a diminishing map of the entire end product produced by all houses ‘ .

In a cournot game, equilibrium is determined at the intersection of both houses ‘ reaction maps[ 2 ]. In other words, the end product chosen by one house, ( say house 1 ) which maximizes his net income, given his beliefs or outlook of the other house ‘s ( say house 2 ) pick is right with the other house ‘s ( steadfast 2 ) pick of end product given his outlook of house 1 ‘s pick [ Pindyck et Al ( 2009:4540 ] and [ Varian ( 2010:508 ) .

P = 359 – 0.10 ( qa + qb )

a = ( P – aA ) qa

a = [ 359 – 0.10 ( qa + qb ) – 109 ] qa

a = 250qa – 0.10qa2 – 0.10qaqb – – – – – – – – – – – – – – ( 1 )

The reaction map for house a is:

a/qa = 250 – 0.2qa – 0.10qb = 0

qa* = 1,250 – 0.5qb – – – – – – – – – – – – – – – ( 2 )

The net income map for house B is:

B = ( P – B ) qb

B = [ 359 – 0.10 ( qa + qb ) – 105 ] qb

B = 254qb – 0.10qb2 – 0.10qaqb – – – — – – – – – – – – – – – – – ( 3 )

The reaction map for house B is:

b/qb = 254 – 0.2qb – 0.10qa = 0

qb* = 1,270 – 0.5qa – – – – – – – – – – – – – – – – – – – ( 4 )

Solving the reaction maps given in ( 2 ) and ( 4 ) at the same time, the equilibrium measures for both houses can be determined therefore:

qa* = 1,250 – 0.5qb

qb* = 1,270 – 0.5qa

qa + 0.5qb = 1,250 – – – – – – – – – – – – – – – – – ( 5 )

qb + 0.5qa = 1,270 – – – – – – – – – – – – – – – – – – ( 6 )

to extinguish qb, multiply ( 5 ) by 2 and ( 6 ) by 1

2qa + qb = 2,500 – – – – – – – – – – – – – – – – – – – ( 7 )

qb + 0.5qa = 1270 – – – – – – – – – – – – – – – – – – – ( 8 )

deducting ( 8 ) from ( 7 ) ,

1.5qa = 1,230

qa = 1,230/1.5

qa = 820 units of the merchandise

Substitute qa = 820 into ( 8 ) to acquire qb ;

qb + 0.5qa = 1,270

qb + 0.5 ( 820 ) = 1,270

qb + 410 = 1,270

qb= 1,270 – 410

qb = 860 units of the merchandise

But industry end product ( Q ) = qa + qb = 820 + 860= 1680 units of the merchandise.

And Cournot monetary value = 359 – 0.10 ( qa + qb ) = 359 – 0.10 ( 820 + 860 ) = ?191

Cournot nash equilibrium result in net incomes can be gotten by replacing both equilibrium measures into the net income maps in ( 1 ) and ( 3 ) .

Net income for house a = 250qa – 0.10qa2 – 0.10qAaqb

= 250 ( 820 ) – 0.10 ( 820 ) 2 – 0.10 ( 820 ) ( 860 )

= 205,000 – 67,240 – 70,520

= ?67,240

Net income for house B = 254qb – 0.10qb2 – 0.10qaqb

= 254 ( 860 ) – 0.10 ( 860 ) 2 – 0.10 ( 820 ) ( 860 )

= 218,440 – 73,960 – 70,520

= ?73,960

Industry net income ( ) = a + B = ?67,240 + ?73,960 = ?141,200.

## GRAPHICAL REPRESENTATION OF REACTION FUNCTIONS IN A COURNOT MODEL

qb

2500 qa* ( qb ) = Firm a ‘s reaction map

1270 A cournot equilibrium

860 qb* ( qa ) = Firm B ‘s reaction map

820 1250 2540 qa

FIGURE 1

The diagram above ( figure 1 ) shows the cournot equilibrium and the reaction map curves of both houses. qa* ( qb ) shows the end product of house a ( qa ) in footings of house B while qb* ( qa ) shows the end product of house B in footings of house a. Point ‘A ‘ represents the cournot nash equilibrium ( measure ) .

If steadfast ‘a ‘ is rational and believes that house ‘b ‘ is besides rational, so he ( tauten a ) will ne’er anticipate steadfast ‘b ‘ to bring forth more than 1,270 units of the merchandise while steadfast ‘b ‘ will ne’er anticipate steadfast ‘a ‘ to bring forth more than 1,250 units of the merchandise.

In drumhead, given the market demand map, P=359 – 0.10 ( qa + qb ) and fringy costs equal to ?109 and ?105 to tauten a and B severally, the cournot nash equilibrium result in net incomes ( ) where ??›± = ( a + B ) =?67,240 + ?73,960 = ?141,200.

## ( degree Celsius )

## NASH EQUILIBRIUM OUTCOME IN PROFITS IN A STACKLEBERG GAME

This is besides a measure based theoretical account which adopts the leader-follower manner. This means that the leader moves foremost while the follower reacts to this first move ( the end product determination of the leader ) .

Given P= 359 -0.10Q

P = 359 – 0.10 ( qa + qb )

And net income map ( p -ci ) chi

For house ‘a ‘

a= 359 – [ 0.10 ( qa + qb ) – 109 ] qa

= 250qa -0.10qa2 – 0.10qaqb – – – – – – – – – ( 1 )

While that of house be is given as ; B = 359 – [ 0.10 ( qa + qb ) – 105 ] qb

= 254qb – 0.10qaqb – 0.10qb2 – – – – – – – – – ( 2 )

reaction map of house ‘b ‘

b/qb= 254 – 0.10qa – 0.2qb

= 1,270 – 0.5qa – – – – – – – – – – ( 3 )

The stackleberg nash equilibrium is gotten by replacing the reaction map of the follower ( steadfast ‘b’- ( 3 ) above ) into the net income map of the leader ( steadfast ‘a’- ( 1 ) above ) and distinguishing with regard to the measure of the leader ( qa ) . Therefore ;

a = 250qa – 0.10qa2 -0.10qa ( 1,270 – 0.5qa )

a = 250qa – 0.10qa2 – 127qa + 0.05qa2

a = 123qa – 0.10qa2 + 0.05qa2

a = 123qa – 0.05qa2 – – – – – – – – – – – – – – – – – – – – – – – – – – – – – ( 4 )

Therefore, stackleberg measure is:

as/ qa = 123 – 0.1qa = 0

qa = 123/0.1 = 1,230 units of the merchandise

Firm ‘b ‘ reacts to this first move with:

qb = 1,270 – 0.5qa ( as in 2* above )

= 1,270 – 0.5 ( 1230 )

= 1,270 – 615

qb = 655 units of the merchandise

But stackleberg monetary value is given as: P = 359 – 0.10 ( qa + qb )

P = 359 – 0.10 ( 1230 + 655 )

P = 359 – 188.5

P = ?170.5

Net income of both houses is gotten by replacing the relevant quanties in the their net income maps stated in ( 2 ) and ( 4 ) above. Frankincense:

For house ‘a ‘

a = 123qa – 0.005qa2

= 123 ( 1,230 ) – 0.05 ( 1,230 ) 2

= 151,290 – 75,645

a = ?75,645

For house ‘b ‘ :

B =254qb – 0.10qaqb – 0.10qb2

= 254 ( 655 ) – 0.10 ( 1230 ) ( 655 ) – 0.10 ( 655 ) 2

=166,370 – 80,565 – 42,903

=?42,902

## Therefore, stackleberg net income = ?75,645 + ?42,902 = ?118,547.

## GRAPHICAL REPRESENTATION OF REACTION FUNCTIONS IN A STACKLEBERG MODEL

qb

2460

Qa* ( qb ) = Firm a ‘s reaction map

1230

Stackleberg ‘s equilibrium

655 B Qb* ( qa ) = Firm B ‘s reaction map

1230 2460 qa

FIGURE 2

The diagram above ( figure 2 ) shows the stackleberg equilibrium and the reaction map curves of both houses. qa* ( qb ) shows the end product of house a ( qa ) in footings of house B while qb* ( qa ) shows the end product of house B in footings of house a. Point ‘B ‘ represents the stackleberg Nash equilibrium ( measure ) .

If steadfast ‘a ‘ is rational and believes that house ‘b ‘ is besides rational, so he ( tauten a ) will ne’er anticipate steadfast ‘b ‘ to bring forth more than 1,230 units of the merchandise while steadfast ‘b ‘ will ne’er anticipate steadfast ‘a ‘ to bring forth more than 1,230 units of the merchandise.

## COMPARISON OF STACKLEBERG AND COURNOT OUTCOMES IN PROFIT

As demonstrated, the cournot net income of ?141,200 is greater than the stackleberg net income of ?118,547. Besides, the leader additions by taking end product foremost, ( i. e. 1,230 & gt ; 820 ) while the follower is worseoff ( i. e. 655 & lt ; 860 ) . As a consequence of taking ouput foremost, participant a ‘s net income is ?57,645 ( up by ?8,405 ) while that of participant B is ?42,902 ( down by ?31,058 ) and industry net income is down by a cyberspace of ?22,653 about. Therefore, it will pay the industry for the participants to travel at the same time with no leader since net income with traveling at the same time is higher than that gotten from traveling consecutive.

## ( D )

A trust is the coming together of a group of houses to act like a individual house and maximise the amount of their net incomes. Harmonizing to Varian ( 2010:513 ) , ‘when houses get together and try to put monetary values ( or ) end product so as to maximise entire industry net income, they are known as a trust. ‘ With collusion, the houses will be better away compared to if they operated as individual houses.

## Result IN PROFIT FOR A CARTEL

Given the reverse demand map:

P = 359 -0.10 ( Q ) and the net income map confronting the trust:

??›± = ( P – degree Celsius ) Q = [ 359 – 0.10 ( Q ) – degree Celsius ] Q

In traveling in front to determine the result, the fringy cost for the merged entity has to be determined because the result is dependent on the fringy cost. Since both houses are merged, it means their fringy cost will lie someplace in between their former fringy cost. ( Slightly more or less than their single fringy costs ) . Assuming fringy cost is 107[ 3 ], ( utilizing the leaden mean attack which is 109+105 ) .

2

??›± = [ 359 – 0.10 ( Q ) – degree Celsius ] Q = [ 359 – 0.10 ( Q ) – 107 ] Q

??›± = 252Q -0.10Q2 – – – – – – – – – – – – – ( 1 )

??›± = 252 – 0.20Q

Q

Q =1,260 units of the merchandise

But the trust monetary value is given as: P= 359 – 0.10 ( Q )

P= 359 – 0.10 ( 1260 )

= 359 – 126

= ?233

But result in net income is gotten by replacing the measure ( 1,260 ) in the net income map stated above in ( 1 ) . That is:

??›± = 252Q – 0.10Q2 = 252 ( 1260 ) – 0.10 ( 1260 ) 2

= 317,520 – 0.10 ( 1,587,600 )

= 317,520 – 158,760

## ??›± = ?158,760

## ( Tocopherol )

Tit for cheapness is a signifier of penalty for a repeated non-cooperative game. If either oppositions defect in any period, so the loyal participant will desert in the following period. As noted by [ Bierman & A ; Fernandez ( 1998:194 ) ] , a house could follow a breast for cheapness policy in period two, dependant on the action ( cooperate or defect ) of the other house in period one ( the old period ) . By collaborating it is meant that houses produce the trust measure and by desertion, the cournot measure is produced ( in this theoretical account ) .

Assuming the trust fixes the production quota of each house at say 630 units of the merchandise, both houses would understand that this maximizes their combined net incomes and both will hold an inducement to rip off. Assuming the monopoly net income is ?158,760 for the industry, so it means each participants payoff will be ?79,380 ( i. e. ?158,760/2 ) ( presuming net income is shared every bit ) . Desertion by either participant, with the other sticking to the production quota, will bring forth a net income higher than the monopoly net income ( to the pervert ) while the net income of the loyal participant will be reduced, even below the cournot equilibrium net income. In the words of [ Varian 2010: 517 ] , ‘if you produce more end product diverting from your quota, you make net income ??›±d, where ??›±d & gt ; ??›±m ‘ . ??›±m here denotes single net income in a monopoly ( conniving ) state of affairs.

## Numeric Illustration:

Assuming trust measure = 1260 units of the merchandise

Each participant ‘s measure = 630 units of the merchandise

Cournot measure ( tauten a ) = 820

Cournot measure ( steadfast vitamin D ) = 860

ROUND 1 – BOTH COOPERATE

a= 250 ( 630 ) – 0.10 ( 630 ) 2 – 0.10 ( 630 ) ( 630 )

= 157,500 – 39,690 – 39,690

= ?78,120

b= 254 ( 630 ) – 0.10 ( 630 ) 2 – 0.10 ( 630 ) ( 630 )

= 160,020 – 39,690 – 39,690

= ?80,640

Industry net income ( ??›± ) = a + B = ?78,120 + ?80,640 = ?158,760

ROUND 2 – Bacillus Defect

a = 250 ( 630 ) – 0.10 ( 630 ) 2 – 0.10 ( 630 ) ( 860 )

= 157,500 – 39,690 – 54,180

= ?63,630

B = 254 ( 860 ) – 0.10 ( 860 ) 2 – 0.10 ( 630 ) ( 860 )

= 218,440 – 73,960 – 54,180

= ?90,300

Industry net income ( ??›± ) = a + B = ?63,630 + ?90,300 = ?153,930

ROUND 3 – BOTH DEFECT

a = 250 ( 820 ) – 0.10 ( 820 ) 2 – 0.10 ( 820 ) ( 860 )

= 205,000 – 67,240 – 70,520

= ?67,240

B = 254 ( 860 ) – 0.10 ( 860 ) 2 – 0.10 ( 860 ) ( 820 )

= 218,440 – 73,960 – 70,520

= ?73,960

Industry net income ( ??›± ) = a + B = ?67,240 + ?73,960 = ?141,200

ROUND 4 – BOTH DEFECT

a = 250 ( 820 ) – 0.10 ( 820 ) 2 – 0.10 ( 820 ) ( 860 )

= 205,000 – 67,240 – 70,520

=?67,240

B = 254 ( 860 ) – 0.10 ( 860 ) 2 – 0.10 ( 860 ) ( 820 )

= 218,440 – 73,960 – 70,520

= ?73,960

Industry net income ( ??›± ) =a + B = ?67,240 + ?73,960 = ?141,200

ROUND 5 – BOTH REPENT

a = 250 ( 630 ) – 0.10 ( 630 ) 2 – 0.10 ( 630 ) ( 630 )

= 157,500 – 39,690 – 39,690

= ?78,120

B = 254 ( 630 ) – 0.10 ( 630 ) 2 – 0.10 ( 630 ) ( 630 )

= 160,020 – 39,690 – 39,690

=?80,640

Industry net income ( ??›± ) = a + B = ?78,120 + ?80,640 = ?158,760

## Monetary values AT EACH ROUND

P= 359 – 0.10 ( Q )

P1 = 359 – 0.10 ( 1260 )

=?233

P2 = 359 – 0.10 ( 1490 )

=?210

P3 = 359 – 0.10 ( 1680 )

=?191

P4 = 359 – 0.10 ( 1680 )

=?191

P5 = 359 – 0.10 ( 1260 )

=?233

From the illustration supra, as a consequence of the actions of the participants, increased end product ( from unit of ammunition 1 to round 4 ) will drive monetary value down and besides industry net income. That is, at the terminal of unit of ammunition 4, expected net income would hold been ?635,040 but existent net income is given as ?595,090. This will go on until both houses ‘repent ‘ and produce the fixed measure, say in unit of ammunition 5.

In the instance of a ‘grim scheme ‘ , when one house defects, the loyal 1 goes inexorable. That is, it retaliates by deserting and will ne’er ‘repent ‘ . Suppose participant B defects, say in unit of ammunition 3, he will gain a net income higher than that of the loyal house. But since both houses defect from unit of ammunition 4 onwards, the net income will be changeless and lower than the trust net income till the terminal of clip.

The industry net income when both houses cooperate will ever be greater than that gotten if one or both participants defected at any unit of ammunition of the game. Therefore, in the long tally, deserting is non profitable.

In drumhead, the trust will go on to run because aberrant behavior by one or both participants will ever ensue in an industry net income less than that of the trust.