Topics in Economic Analysis

Alexia GaudeulSpring 2009

Topics in Economic Analysis

5 weeks of lectures2

Programme

Textbooks

Weeks 1 and 2: Choice under risk Week 3: Choice under uncertainty Weeks 4 and 5: The unravelling of markets

with asymmetric information

Kreps, D.M. (1990), “A Course in Microeconomic Theory”, Harvester Wheatsheaf (thereafter `Kreps’).

Holt, C.A. (2007), “Markets, Games and Strategic Behavior”, Pearson Education (thereafter `Holt’)

Choice under riskLotteriesExpected Value Theory

Marschak-Machina triangleAxioms of EUTRisk attitudes and risk aversion

Week 1: Expected Utility Theory

Spring 2009

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Choice under risk

Gamble: Crossing Earlham Road, blindfolded, at 9:00 on a school day. If not crushed by a car, win £100,000. If crushed by a car… the outcome is left to your

imagination (think road kill). Do you accept the gamble? What if you are offered £1,000,000?

Getting insurance, accepting a job offer, going to party before an exam, etc…

Spring 2009Topics in Economic Analysis

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Lotteries

Two possible outcomes (£100,000, Death)

Probabilities (90%,10%)

Lottery denoted as (90%,10%) over the two outcomes

Spring 2009

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£100,000 Death

90% 10%

Expected Value Theory

St Petersburg Paradox

How much would you pay to play? What is the expected value of this lottery?

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Topics in Economic Analysis Spring 2009

£2 £4 £8 £16 £32 £64 £128

1/2 1/2 1/2 1/2 1/2 1/2 1/2

Marschak-Machina Triangle


7

£0£50

£100

A

1/6 probability of 0



Direction of preferences

In the beginning was nothing…


8

£0£50

£100

A

B

A>B or B>A?(one knows nothing)

The completeness axiom


9

£0£50

£100

A

B

Either A>B or B>A(there is an indifferencecurve that separates Afrom B)

A>B

The continuity axiom


10

£0£50

£100

A

B

If A>B>C, then there exists p such that pA+(1-p)C=B(no breaks in indifference curves)

C

The transitivity axiom


11

£0£50

£100

A

B

If A>B and B>C, thenA>C (no crossing ofindifference curves)

C

The independence axiom


12

£0£50

£100

A

B

If A>B then pA+(1-p)C > pB+(1-p)C(indifference curves are parallelstraight lines)

C

Expected Utility Theory


13

If the four axioms above are verified, then u(A)=1/6u(0)+1/2u(50)+1/3u(100)

If u(A)=1/6u(0)+1/2u(50)+1/3u(100), then the four axioms are verified.

If I know the utility of 0, 50 and 100, then I know the utility of A.

If I know the utility of A and the shape of the utility function, then I know how much the agent is ready to pay to play A.

Example (1)


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Suppose your utility function is u(x)=√x Then your utility for the St Petersburg lottery is:

½√2+¼√4+1/8√8+1/16√16+1/32√32+1/64√64+1/128√128+1/256√256+…=2.414213511…

Which means you would be ready to pay (2.414213511…)2=£5.83

Example (2)


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Suppose your utility function is u(x)= 1/2√x. How much are you ready to pay? (answer: the same)

Suppose your utility function is u(x)=ln(x). How much are you ready to pay? (answer: £4)

Example (3)


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0.000010.2

0.40.6

0.81

1.21.4

1.61.8

22.2

2.42.6

2.83

3.23.4

3.63.8

44.2

4.44.6

4.85

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

sqrt ln

Risk attitudes


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The agent with the logarithmic utility function would pay less for the lottery than the agent with the square root utility function.

This agent is therefore more risk averse. How can we explain and measure risk aversion?

Risk aversion and certainty equivalent


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U(x)

x£1 £10

A

£3

I am ready to pay £3 to play A,a lottery with proba 1/2 of £1 and proba 1/2 of £10

Risk premium


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U(x)

x£1 £10

A

£3

I am ready to pay £2.5 LESS than the expected value of A to play A. This is my risk premium.

£5.5

Experimental evidences against EUTAlternatives to EUT

Week 2: EUT anomalies20


Experimental evidences against EUT


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The Allais Paradox and the independence axiom P-bet and $-bet and the transitivity axiom Ambiguity aversion, the Ellsberg paradox and the

‘Sure Thing Principle’ Framing effects and moral problems

Alternatives to EUT


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Psychological probabilities and Prospect Theory The use of editing algorithms and the Rank

Dependent Expected Utility Model Lottery comparisons and Regret Theory

The Allais Paradox (1)


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Choose between A and B. Choose between C and D.

A B C D£4,000 80% 0% 20% 0%£3,000 0% 100% 0% 25%

£0 20% 0% 80% 75%(Kahneman and Tversky, 1979)



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According to EUT, if you chose B over A, then this means that u(3000)>0.8u(4000)+0.2u(0).

But then 0.25u(3000)>0.2u(4000)+0.05u(0). Therefore,

0.25u(3000)+0.75u(0)>0.2u(4000)+0.80u(0). So D must be preferred over C.



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In reality, while about 80% prefer lottery B over lottery A, only 35% prefer lottery D over lottery C.

I therefore cannot have y equal to 0. This means some people reverse their preferences.

Note that I might have x=0.

C>D D>CA>B w x 20%A<B y z 80%

65% 35%

$-bet and P-bet


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Which one do you prefer? P-bet: £8 with 60% probability $-bet: £18 with 30% probability (from Loomes, Starmer and Sugden, 1991)

How much would you be prepared to pay to play the P-bet? The $-bet?

Suppose I offer you £4 to play the P-bet? Do you accept? What about the $-bet?

Do you see an issue with your answers to the three questions? Are they consistent?

Ellsberg paradox (1)


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Choose between A and B. Choose between C and D.

33.33%red blue or green

A £1,000 £0 £0B £0 £1,000 £0C £1,000 £0 £1,000D £0 £1,000 £1,000

66.67%



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Most people choose A over B, and then D over C. This contradicts Savage’s “Sure Thing Principle”:

adding up the certainty of having £1000 in case the ball is green should not change the choice of the agent.

Check that if we assign ‘subjective’ probability p(blue) and p(green) to having a blue or green ball respectively, then, according to EUT, agents who choose A over B should choose C over D.



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Therefore, some agents do not reason based on a subjective evaluation of probabilities (as offered by Savage in his theory of subjective expected utility).

In the case above, one can argue that agents dislike facing uncertainty, which are situations where one does not know what objective outcome probabilities one is facing.

This is called ambiguity aversion. Ambiguous situations are ubiquitous however.

Ambiguity aversion


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While most of the time one dislikes ambiguity, sometime one prefers it.

Example: Testing for AIDS and other STD. Many people will prefer not knowing whether they have AIDS or not. They may also prefer not to know whether their partner has a STD or not.

The same holds with ‘what might have been’ statements: Suppose you had the opportunity to join a rock band when you were 16, but you didn’t. You spend the next 50 years as an obscure, bitter and frustrated lowly-paid employee. Would you like to know how successful that rock band would have been?

Framing effects


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A train is going to kill 5 people on a track. You have the opportunity to pull a lever and divert the train to another track where there is only 1 person. Do you do it?

A train is going to kill 5 people on a track. You have the opportunity to push a person under the train and thus stop it. Do you do it?

For more moral questions, go to the Moral Sense Test, http://moral.wjh.harvard.edu/, by Marc D. Hauser.

See also articles by Peter Singer, Princeton.

http://moral.wjh.harvard.edu/�

Other Moral Problems


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Suppose you have to plunge 5 feet (1.5 meters) to save a complete stranger from drowning. Do you do it? What about 10 feet (3m)? 20 feet (6.1m)?

Suppose you reject plunging 20 feet. What about if it is a friend? 40 feet (12.2m)?

Suppose you reject plunging 40 feet for a friend. What if it is your child? 60 feet (18.3m)? (Wicksteed, 1910, Bk 1, Ch. 1, #24)

Is EUT and the concept of lotteries the right way to think about those issues?

http://www.econlib.org/library/Wicksteed/wkCSCover.html�

Prospect theory (1)


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Rather than u(A)=0.25u(10)+0.75u(5), one writes u(A)=f(0.25)u(10)+f(0.75)u(5)

f(.) is the probability weighting function. It reflects that agents OVERweigh LOW probability

events and UNDERweigh HIGH probability events. It may be that agents are not used to evaluating

events that do not occur often.

Prospect theory (2)


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Objective probability x

Subj

ectiv

e pr

obab

ility

y

y=x

Probability weighting function y=f(x)

1/3

Prospect theory (3)


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Agents overestimate the probability of rare events, so they overestimate the probability to win a state lottery (low probability event) or underestimate the probability they won’t be crushed by a car (high probability event).

One can thus see the same person buying a lottery ticket (risk loving) and buying car insurance (risk averse), which under EUT makes no sense at all.

Prospect theory (4)


36

From the above (change in attitudes to risk), one can thus explain fanning OUT with prospect theory.

£0£50

£100

A

B

C

Rank dependent EUT (1)


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Rank dependent expected utility comes from the observation that people do not react the same with ‘losses’ and ‘gains’.

In a first step, outcomes are ranked in terms of their desirability.

A cut point is chosen, separating those outcomes that are ‘losses’ and those that are gains.



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A different utility function is applied to ‘gains’ and to ‘losses’.

Example: Outcomes are -£1000, £0 and £5000. Suppose £0 is considered as a loss. Then the utility of a lottery with proba 1/3 of each

event is 1/3L(-1000)+1/3L(0)+1/3G(5000).

Contrary to EUT, I do not necessarily have L(-x)=-G(x).



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losses gains

An agent that might be almost risk neutral with respect to gains may be strongly risk averse when it comes to losses.

G(x)

L(x)

utility

Regret theory (1)


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A is a coin-toss over (-£100,+£100), B is a coin-toss over (-£900, £9000). The two coins are tossed independently, and you learn the outcome of both coin-tosses. However, you must choose between A and B before the coins are tossed.

In an imaginary future world, this results in four possible events, with probability ¼ each.

-£100 £100

-£900 ¼ ¼

£9000 ¼ ¼

Regret theory (2)


41

The expected ‘regret’ of choosing A over B is 1/4r(-100,-900)+1/4r(-100,9000)+1/4r(110,-

900)+1/4r(110, 9000)

r(-100,-900) is high, as you avoided losing £900 and only lost £100.

But what about r(110,9000)? Then this is very low: you may have won in A but you could have done much better choosing B.

Issues with risk aversion within the setting of EUT


42

Suppose I own £1000 and my utility function is of the form u(x)=ln(x).

Suppose I am offered the prospect of playing a lottery with proba 1/2 to get £110 and proba 1/2 to lose £100.

My utility from taking the lottery is 1/2ln(1000-100)+1/2ln(1000+110) This is less than ln(1000), the utility of not taking the

lottery, so I reject the lottery.

Issues with risk aversion (2)


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But this also means I would reject a lottery offering proba 1/2 to get £9000 and proba 1/2 to lose £900 (Rabin, 2000)

Is this reasonable, when the Expected Value of this gamble is £4050?

Does EUT provide the right tool to think about risk aversion?

Key concepts for weeks 1 and 2

Expected value St Petersburg

paradox, Expected utility Risk aversion Allais paradox WTA/WTP disparity Sure thing principle

Ellsberg paradox Ambiguity aversion Regret theory Rank dependent

expected utility Weighted utility Prospect theory

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References (weeks 1 and 2)

Textbook readings: Kreps, Ch. 3 Holt, Ch. 4, pp. 50-54, risk aversion in an experimental setting Holt, Ch. 28, anomalies in EUT

Essential readings: Starmer C.V. (2000): “Developments in Non-Expected Utility Theory: The

Hunt for a Descriptive Theory of Choice under Risk”, Journal of Economic Literature 38, pp. 332-82.

Other references: The Moral Sense Test, a Web-based study into the nature of human

moral judgment, http://moral.wjh.harvard.edu/ On applications of utilitarianism (consequentialism) to bioethics, consider

reading “Practical Ethics” by Peter Singer, Cambridge University Press, 1993.


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http://www.jstor.org/stable/2565292�


http://moral.wjh.harvard.edu/�

Optional readings

Camerer C. (1995): “Individual Decision Making”, in J. Kagel and A. Roth (eds.), Handbook of Experimental Economics, Princeton University Press, pp. 596-602 and 609-612 (on probabilistic anomalies) and pp. 644-649 (on choice under uncertainty).

Gravelle H. and R. Rees (1992): Chs. 19-20 in “Microeconomics”, Longman: London, pp. 557-575, 586-590, 594-599, 606-608.

Kahneman D. and A. Tversky (1979): "Prospect Theory: An Analysis of Decision under Risk", Econometrica, 47(2) pp. 263-291.

Loomes G., Starmer C. and R. Sugden (1991): "Observing Violations of Transitivity by Experimental Methods", Econometrica, 59(2), pp. 425-439.

Machina M. (1987): “Choice Under Uncertainty: Problems Solved and Unsolved”, Journal of Economic Perspectives 1, pp. 121-154.

Rabin M. (2000): ''Risk Aversion and Expected-utility Theory: A Calibration Theorem'', Econometrica, 68(5), pp. 1281-1292

Wicksteed P.H. (1910): "The Common Sense of Political Economy", Macmillan and Co.: London, 1st Edition. esp. Book 1, Chapter 1, #24. for the "plunging" experiment.


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http://www3.interscience.wiley.com/journal/119003388/abstract�


http://www.econlib.org/library/Wicksteed/wkCSCover.html�

A simple entry game?A not so simple entry gameRationalizing irrational behavior and the limits of rationality

Week 3: Incomplete information, reputation and irrationality

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A simple entry game (1)


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The situation in extensive form The situation in normal form The editing of Nash equilibria by backward

induction Can the incumbent ever deter entry?

A simple entry game (2)


49

An incumbent derives monopoly profit of 4 from its market.

A firm comes in and can invest 1 in entering the market.

If it invests 1, then firms may set up a collusive agreement and share monopoly profit of 4.

If instead the incumbent chooses to fight, then Bertrand competition occurs and they both make zero profit.

Entry game in extensive form


50

Entrant

Incumbent

Not enter

Enter

Accommodate

Fight

( 0 , 4 )

( 1 , 2 )

( -1 , 0 )

Entry game in normal form


51

Two pure strategy Nash Equilibria, (E,A) and (NE,F). A range of mixed strategy Nash Equilibria such that

(NE, Prob(Fight)>1/2)

Accommodate Fight

Enter 1 , 2 -1 , 0

Not enter 0 , 4 0 , 4

Backward induction


52

Is it reasonable for the incumbent to fight once the entrant entered? NO.

Therefore, it is not reasonable for the entrant to expect the incumbent to fight once it entered.

Therefore, any equilibria that involve the incumbent fighting are not sustainable.

The only Nash equilibrium that survives backward induction is (E,A): there is no way for the incumbent to credibly deter entry.

Entry deterrence


53

How could the incumbent deter entry in a credible way? The incumbent could buy up any entrant... The incumbent could sell more than monopoly quantity

so as to decrease potential profits for an entrant... The incumbent could increase the cost of entry from 1 to

a number more than 2 (imposition of high quality standards, acquiring patents on essential technology, vertical control of the supply and retail chain, etc).

A not so simple entry game


54

The Kreps-Wilson-Roberts (‘KWR’) reputation story: Two types of incumbents: crazy or sane. The crazy

incumbents always fight. Why it may make sense for the entrant to believe some

incumbents are crazy. Why it may make sense for the sane incumbent to act

crazy. What do we mean by crazy behavior? Is it rational to

sometime act crazy? When is that?

Crazy incumbents


55

An incumbent may be crazy (fight all the time), because: Managers are rewarded on sales, not profits. It expects the entrant to back out. It is diversified and wants to signal that entry is not

acceptable in other markets either. It actually has lower costs than expected by the incumbent

and can still make profit under Bertrand competition. Its managers are egomaniacs, hold grudges or are

otherwise irrational and ignorant (i.e. they did not study economics).

The KWR reputation story (1)


56

Entrant

Incumbent

Not enter

EnterAccommodate

Fight

( 0 , 4 )

( 1 , 2 )

( -1 , 3 )

Entrant

Incumbent

Not enter

EnterAccommodate

Fight

( 0 , 4 )

( 1 , 2 )

( -1 , 0 )

Nature

CrazyIncumbent

Sane incumbent



57

In a separating equilibrium, the sane incumbent accommodates and the crazy one preys.

If the probability the incumbent is crazy is p, then the entrant’s expected payoff when it enters is -p+(1-p), which is less than 0, the payoff of not entering, as long as p>1/2.

So if p>1/2, then the entrant does not enter. The entrant’s payoff is 0, the incumbent’s payoff is 4.



58

Suppose now the game is repeated twice, and p<1/2. A separating equilibrium is such that the sane incumbent

accommodates and the crazy one preys. Then the entrant enters in both periods. This is a Bayesian Nash Equilibrium as no one has a (strict) individual incentive to deviate from such strategies.

A pooling equilibrium is such that the crazy incumbent preys in both periods, while the sane incumbent preys only in the first. Then the entrant would stay out in the first period and enter in the second. This is a BNE but not a rationalizableone, since if the entrant played out of equilibrium and entered in the first period, the sane incumbent would actually accommodate.



59

Suppose now the entrant believes the sane incumbent fights in the first period with some probability 1>s>0. Note that the separating equilibrium is a special case

where s=0, while the pooling equilibrium is a special case where s=1.


Given belief s, the probability to face a fight in the first period is: p(fight) = p(fight and sane)+p(fight and crazy)

=p(fight/sane)p(sane)+p(fight/crazy)p(crazy) = s(1-p)+p.

Therefore, the entrant will not enter in the first period when it expected payoff, -1(s(1-p)+p)+(1- s(1-p)-p) is less than 0.

This translates in not entering in the first period if s>(1/2-p)/(1-p).

However, there is entry in the second period.


60


This belief s can however be rationalized (sustained) only if the incumbent would actually fight with probability s in the first period if challenged by the entrant… This is the case only if fighting in the first period induces the

entrant not to enter in the second period. Otherwise, the sane incumbent would not fight (loss of

payoff and no deterrence). Consider thus the entrant who was faced with a fight in

the first period. After a fight, the entrant believes the incumbent is crazy with probability p(crazy/fight)=p(crazy and fight)/p(fight)=p/(s(1-p)+p).


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The entrant faced with a fight in the first period will thus not enter in the second subject to its expected payoff in the second period being negative -1(p/(s(1-p)+p))+1(1-p/(s(1-p)+p))<0

This can be rewritten as s<p/(1-p). Intuitively, if the sane incumbent fights too often,

then fighting loses its power of signalling the incumbent is crazy.


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Finally, the sane incumbent must fight in the first period with probability s, which is the case only if it is indifferent between fighting and not fighting. Its expected payoff of fighting is 0+4 if s<p/(1-p) (entry is deterred in the second period) and 0+2 if s>p/(1-p) (entry is not deterred in the second period) to be compared with 2+2 if it does not fight in either period.

Therefore, the incumbent fights with probability s in the first period only if s<p/(1-p).

Any belief such that s>p/(1-p) is not sustainable.


63

KWR summary: BNE


64

1/2 p

s

1/2(1/2-p)/(1-p)

No entry in first periodEntry in second period

Entry in both period

No entry in either period

Entry in first periodExit if faced with fight

p/(1-p)

KWR summary: Rationalizable BNE


65

1/2 p

s

1/2

p/(1-p)

(1/2-p)/(1-p) No entry in first periodEntry in second period

Entry in both periodsNo entry in either period

Entry in first periodExit if faced with fight

KWR summary


66

If p>1/2: then the entrant never enters. Payoff for the sane incumbent is 4+4

If p<1/2: If s<p/(1-p) and s>(1/2-p)/(1-p), then the entrant will not enter in the

first period, though it will enter in the second as p<1/2. Payoff for the incumbent is 4+2.

If s<p/(1-p) and s<(1/2-p)/(1-p), then the entrant will enter in the first period, and the sane incumbent will fight with probability s. If faced with a fight, the entrant does not enter in the second period. Payoff for the incumbent is 0+4 if it fights (proba s), 2+2 if it does not.

If s>p/(1-p), then there is entry and no fight in both period. Payoff for the incumbent is 2+2.

All thus depends on what belief s is. Note that s is NOT under the control of the incumbent (otherwise, would choose s=1!)

Discussion of KWR


67

KWR explains apparently ‘irrational’ behavior by a concern for reputation, itself brought about by a concern for the future.

Is that actually irrational behavior? Yes if one considers only one period payoffs, no otherwise.

However, KWR show that imitating irrational behavior can be rational in some situations.

This is an observation that can be extended to other areas. One could for example study the rationality of herd behavior such as when trading in a bubble market.

Beer-Quiche Game (1)


68

The Beer-Quiche game is a signalling game, played over one period only.

A man walks in a bar... he can be either strong or weak. The strong prefer drinking beer and the weak prefer eating quiche.

However, a bully is around and enjoys beating the weak, though, like all bullies, he is a coward and would avoid fighting the strong.

If the strong and the weak both chose their preferred choice, then the strong would drink beer, the weak would eat quiche, and the weak would be identified by his choice and attacked by the bully.

Beer Quiche Game (2)


69

The weak may then prefer to drink beer, even though he does not like this as much as eating quiche, just to avoid being beaten up.

If he does so though, he may be attacked anyway, because drinking beer loses its signaling value (as in the entry game).

The strong man may then start eating quiche, because he does not want to be seen as a weak who drinks beer just to look strong!

However, if so, then, the weak man will switch back to eating quiche to look like a strong man who does not want to be seen as a weak who drinks beer just to look strong!!!

There are thus no separating equilibria. Either both eat quiche, or both drink beer. Those are two possible pooling equilibria.

Beer-Quiche Game (3)


70

The ‘intuitive criterion’ (Cho and Kreps, 87) says that the only reasonable pooling equilibrium is such that it does not rely on believing a dominated strategy would be played out of the equilibrium path.

This means that both eating quiche, which is sustained only by the bully believing that only the weak would drink beer out of the equilibrium path, is not reasonable.

Indeed, only the strong could benefit from drinking beer instead of quiche (there is a fight anyway, but at least he gets his beer!).

Both drinking beer is fine however, as only the weak could benefit from eating quiche, so believing the out of equilibrium quiche eater is weak and therefore attacking the quiche eater is reasonable.

This ‘intuitive criterion’ does not perform well in experimental settings however.


Rationalizing irrationality


71

The centipede game (a.k.a. game of trust or investment game). Equilibrium by backward induction. What happens if there are a few naïve or inattentive

players? A theory for market instability, bubbles and crashes?

The centipede game (1)


72

Also called investment game. I have £1. I can keep it or lend it to you, which will

generate £2. You can then choose to keep all of it for yourself or give it back to me.

If you give it back to me, then this generates £4… I can then either keep this or lend it back to you…

And so on… at the end, one can either choose to share equally, or keep everything.



73

A three stage centipede game

( 1 , 0 ) ( 0 , 2 ) ( 4 , 0 )

( 2 , 2 )

Keep Keep Keep

Lend Lend Share1 12



74

By backward induction, one can see that the equilibrium is such that one keeps all the time.

However, from an experimental viewpoint, this is not what happens.

People tend to cooperate in the first few period, until the equilibrium breaks down at some point.

Sometime, cooperation is sustained up until the end (McKelvey and Palfrey, Econometrica, 1992)

http://links.jstor.org/sici?sici=0012-9682(199207)60:4<803:AESOTC>2.0.CO;2-J�



75

There are several possible explanations for cooperative behavior in the centipede game: People do not reason by backward induction. People reason by backward induction but are not sure

others do. People are concerned about equity as well as their own

payoffs (social preferences, see end of lecture handout).

People just do not understand what the game is about. People follow some ingrained social rules that mandate

repaying what was given.



76

Let us consider agent 1 who believes that with probability p she will be lent back the £2 by 2.

In the last period, she keeps the money so she gets £4 (rational).

In the first period, she lends if 4p, the expected payoff of lending, is more than 1, the payoff of keeping.



77

However, p may be the probability 2 is irrational, in this case, always repays.

This is thus a setting with two types of players, irrational and rational, and agents do not know the type of other agents.

Then a rational agent may play like an irrational one (lend) in the hope of having met an irrational agent.



78

There is no need necessarily to have any irrational agent...

One could have everybody rational and yet acting as if they were irrational in the belief some other agents are irrational.

This belief can be maintained if it benefits all parties. There is no point shattering that belief.

The only question is at what point to break the illusion. This all depends on how many other irrational agents one believes to be. This can be learned over time.

Note the link with Keynesian thinking (“animal spirits”, changes in moods, explain fluctuations)

Social preferences (1)


79

Social preferences are one other possible explanation for trust in the investment game.

Formally, if one receives x and the other y, then one’s utility may be U(x,y)=u(x)+su(y). If s>0, then this is altruism (s>1 is self-denial, one is better

off giving everything to the other!) If s<0 then this is envy. 1 will share in last period if U(2,2)>U(4,0) or

(1+s1)u(2)>u(4)+s1u(0). Normalizing u(0) to 0, I must have s1>u(4)/u(2)-1. If u(x)=√x, then this translates in s1>0.41.

Social preferences (2)


80

If this is the case, then 2 will lend back if U(2,2)>U(2,0), or (1+s2)u(2)>u(2), which is the case if s2>0.

Finally, 1 will lend in the first period if U(2,2)>U(1,0), which is implied by U(2,2)>U(4,0).

Therefore, I only need 2 not to suffer from envy (a cardinal sin!) (s2>0), while 1 must have a stake in the welfare of the community (s1>0.41): a priest, a banker or the taxman?

A guessing game (1)


81

How do people play games of beliefs with imperfect common knowledge: Choose a number between 0 and 100 Write it down on paper, without showing your

neighbors When asked, tell me your choice. I will compute the average choice of the class. I will then multiply that average by 2/3 The winner will be the one who chose the number

closest to 2/3 of the average choice of the class

A guessing game (2)


82

Name Choice

Adelina 50

Kenneth 20

Dusayee 45

Tina 67

Alexia 36

Average 44

2/3*44=29

Alexia wins (predictably...)

A guessing game (3)


83

Who is cleverer, the one who plays the Nash equilibrium (0), or the one who actually won?

How does one choose a number? Suppose the class average is 50, and in another

class, the average was 40. What does that tell us about both classes?

What would happen if we played the game again? Read Nagel R. (1995): “Unraveling in Guessing Games:

An Experimental Study”, The American Economic Review, 85(5), pp. 1313-1326.



Key concepts for week 3

Nash Equilibrium Backward Induction Subgame Perfect Nash

Equilibrium Perfect Bayesian Nash

Equilibrium Beliefs

Centipede game Game of trust Entry game Rationality and

irrationality

84


References (week 3)


85

Textbook readings: Kreps, Ch. 12-13 Holt, Ch. 23

Essential readings: Gibbons R. (1992): “A Primer in Game Theory”, contains a

good discussion of the game theory concepts used in the lectures.

Milgrom P. and J Roberts (1982): “Predation, reputation, and entry deterrence”, Journal of Economic Theory, vol. 27, pp. 280-312

http://www.polisci.ucsd.edu/~bslantch/courses/pdf/milgrom-jet1982v27n2.pdf�

http://www.polisci.ucsd.edu/~bslantch/courses/pdf/milgrom-jet1982v27n2.pdf�

Optional readings


86

Cho I-K and D.M. Kreps (1987): "Signaling Games and Stable Equilibria", The Quarterly Journal of Economics, 102(2), pp. 179-221.

McKelvey R.D. and T.R. Palfrey (1992): "An Experimental Study of the Centipede Game", Econometrica, 60(4), pp. 803-836

Milgrom P. and J. Roberts (1982): “Limit pricing and entry under incomplete information: an equilibrium analysis”, Econometrica, Vol. 50, pp.443-459

Ariely D. (2008) "Predictably Irrational: The Hidden Forces That Shape Our Decisions", HarperCollins Publishers Ltd. (A good outline is available here).

Rosenfeld A. (2008): "Pay It Backwards: An Act Of Coffee Kindness", The Huffington Post, December 23, 2008 (An amusing illustration of a centipede game.)

Economic Classroom Experiments/Guessing Game, an explanation and some evidences on the guessing game, at Wikiversity, http://en.wikiversity.org.




http://links.jstor.org/sici?sici=0012-9682(198203)50:2<443:LPAEUI>2.0.CO;2-E�

http://links.jstor.org/sici?sici=0012-9682(198203)50:2<443:LPAEUI>2.0.CO;2-E�

http://bookoutlines.pbwiki.com/Predictably-Irrational�

http://www.huffingtonpost.com/arthur-rosenfeld/pay-it-backwards-an-act-o_b_151793.html�

http://en.wikiversity.org/wiki/Economic_Classroom_Experiments/Guessing_Game�

http://en.wikiversity.org/�

Akerlof’s “market for lemons”Reputation, signaling, guarantees and certificationSpencer’s educational screening

Week 4: Adverse selection and market failures

87


The Market for Lemons (1)


88

Akerlof’s “market for lemons” (1970) or “the case of the disappearing market”.

Consider a buyer faced with many sellers i={1,…,N}, each with a good of quality qi, qidistributed over [0,1] according to the uniform distribution function.

qi is known to the buyer i only and not to others. The buyer is a price taker: she buys s.t. her

expected payoff being more than 0.




89

She derives utility qi from buying a car of quality qi. The seller i derives utility qi from his own car. Suppose the buyer is offered a price pi by seller i. She then knows that quality qi is at least less than pi. Therefore, the expected value of the car is pi/2. Therefore, if she accepts, she gets expected utility -

pi/2.



90

The buyer rejects any offered price pi>0. Therefore, only the seller with a car of quality qi=0

will sell. Only lemons sell, while all other cars stay on the

market. The process above is called ‘unraveling’. There is no point for the seller to produce a car of

better than lowest quality. Or is there?...

How to guarantee the existence of markets?


91

Despite Akerlof’s prediction, markets for used cars do exist. How is that? Reputation, in the context of a repeated game with

many players, credible ex-post information and common knowledge.

Signaling through advertising Guarantees and the ability to commit Certification by intermediaries

eBay (1)


92

eBay (2)


93

Policy of eBay to encourage positive feedback. Negative rating very rare but given same weight as

positive. Allows explanation for negative ratings. Encourages private negotiation before bringing

disagreements in the open. Fear of retaliation if negative feedback given.

eBay’s reputation system works only in practice (not in theory)!

eBay (3)


94

However, even though very few negative feedback given: “Stoning”: a seller who gets negative feedback

increases its chance to get negative feedback next. Sellers who get a negative rating will decrease their

effort and / or change their prices and / or quit and come back under a new identity.

For more on this, see Dellarocas (2006)

http://www.rhsmith.umd.edu/faculty/cdell/papers/onlineopinionforums.pdf�

The forum: intermediating word of mouth.


95

Seller

Buyer 1 Buyer 2

Sells

Tells

Buys

Forum

Reports

Punishes / Rewards5

1 4

32

6

Reputation (1)


96

Reputation is a system that is used by a number of intermediaries on the Internet to discipline their sellers.

For example, on Amazon.com, consumers can give their feedback on the independent sellers that Amazon.com hosts.

When one looks at those feedbacks, one finds that most sellers have close to perfect feedbacks.

Why? Sellers with lower feedback are eliminated from consideration by consumers.

Reputation (2)


97

How does the system work? The feedback from other buyers must be credible i.e. the experience of past buyers must be relevant to you, i.e.

commonality of aims and preferences. the system must be robust to manipulation: by the seller, i.e. no way to delete bad feedback. by the intermediary, i.e. no way for the seller to get the

intermediary to delete bad feedback. by the buyer, i.e. no way for the buyer to threaten to lie just to get

a lower price. by the competitors, i.e. no way for the competitors to leave bad

feedback on the seller.

Advertising (1)


98

Consider now a modified market for lemons, with two possible quality levels, qH>qL, that cost c(qH) and c(qL) to produce respectively, with c(.) an increasing function and c(q)<q for any q.

The seller does not derive utility from his product. The seller of a good of quality qH must spend a if he

wants to advertise his good. The seller of a good of quality qL must spend A>a to

advertise his good. Advertising is undifferentiated between good and bad

products (pure signaling).

Advertising (2)


99

Suppose qH>pi>c(qH) and there is no advertising. Then I do not know if the good is of high or low quality. If I bought in equilibrium, then sellers would start producing lower quality, so there is no such equilibrium.

Suppose now c(qH)>pi>c(qL) and there is no advertising. Then it must be that the good is low quality, and I will not buy. I buy only as long as pi<c(qL). So there is no point producing high quality.

Suppose though that i produces a good of good quality and spent a in advertising and sets qH>pia>c(qH) and pia-c(qH)-a>0.

Advertising (3)


100

Suppose I buy at price pia when I observe advertising, but not at any price pi >c(qH) if I do not observe advertising. Then producers of goods of quality qH may do advertising.

However, one must ensure that the low quality seller will not imitate the high quality sellers and do advertising.

This is so as long as pi, the price without advertising, is such that pi-c(qL)>pia-c(qL)-A.

I must thus have A>pia-pi. I must also have pi-c(qL)=pia-c(qH)-a, else all would either make low or high quality products.

Advertising (4)


101

This means that c(qH)-c(qL)=pia-pi-a. Therefore, I can have differentiated prices and quality

levels if there is a credible signaling mechanism to differentiate the two types of products.

Advertising does not have to be informative, i.e. no need to ‘prove’ quality of product.

Advertising is credible here because 1) the high and low quality sellers have to expend different levels of advertising 2) Buyers observe advertising accurately (common signal)

For more on this topic, see Nelson (1974).


Guarantees (1)


102

Suppose the seller can offer a guarantee g(pi) such that g(pi) is given to the consumer if she paid pi and comes back to return the good and alleges it is of lower quality than expected. Suppose she can prove so and there are no costs to returning the good.

For example, g(pi)= pi corresponds to a full reimbursement.

Suppose seller i with a good of quality qi who asserts his good is of quality qi can sell it at price pi(qi).

Guarantees (2)


103

If seller i deviates and asserts his good of quality qiis actually of quality qJ then the consumer returns the good, and the profit of the deviator is pi(qJ)-g(pi(qJ)).

This must be no more than the profit from telling the truth, which is pi(qi)-c(qi).

I must thus have pi(qJ)-g(pi(qJ))<pi(qi)-c(qi) for the guarantee to be fully effective.

If it is, then p(q)=q for any q as the buyer is a price taker.

Guarantees (3)


104

Suppose c(q)=c*q with c<1 the marginal cost, same for all.

Suppose also g(x)=g*x with g in [0,1] The supplier could say q=1 so I must have 1-g<(1-c)*q

for this to be avoided. Rewrite this and you find that I must have g>1-(1-c)*q. This must be true even if q=0, so I need g=1. This means a full guarantee is necessary, so as to deter

deviation by the worst sellers. For more on this topic, see Heal (1977).


Guarantees for informational goods


105

Consider now a modified situation where the good has to be consumed for its quality to be known: ice cream, software, book, ...

I cannot wipe out your experience of a book when you come back for a refund. Therefore, whether you liked the book or not, you ask for a refund.

To avoid this, samples may be given to you (one spoon, one month, one page...)

How do you make sure the sample is representative of your future experience?

Certification (1)


106

Suppose an intermediary comes in and offers to certify the goods.

The intermediary knows the quality of the goods and cannot lie, but it can be vague.

For example, instead of saying: “this good is of quality qi ”, it can say, “this good is of quality between [a,b]”, which is true as long as qi∈[a,b], or ‘this good is not of quality qJ’, which is true as long as qi≠qJ, or it can choose to say nothing.

Certification (2)


107

Suppose the certification intermediary offers to sells its services at price t to each sellers who comes to get certified.

Suppose it offers to tell the consumers the quality of the good.

Then, a seller with a good of quality q can choose to get certified, sell at price p(q)=q and make profit of p(q)-t.

Otherwise, it can choose to not get certified, sell as market price P and make profit P.

Certification (3)


108

Then, all sellers with a good with quality q s.t. q-t>P will get certified.

That means that any seller with good of quality q<P+t will not get certified.

Therefore, the expected value of a good that is not certified is (P+t)/2 (remember we still assume uniform distribution).

Therefore, P= (P+t)/2, so P=t. This means that all sellers with quality more than 2t

get certified, and others don’t.

Certification (4)


109

Profit for the intermediary is then (1-2t)t. This is maximized for 1-4t=0 or t=1/4. This means half get certified, half don’t. Is there no way to do better, by for example NOT

saying the whole truth? YES. The best for the certifier is say “this good is not of

quality 0” as long as this is indeed true, and say “this good is of quality 0” if this is indeed true.

Suppose all those with quality more than 0 get certified.

Certification (5)


110

In that case, getting certified allows you to sell at price 1/2 (expected value if certified) and make profit 1/2-t. Not getting certified gets you identified as a 0, with 0 profit.

This means the intermediary can set t=1/2 and make corresponding profit 1/2 which is more than 1/8 if it just told the whole truth.

This depends of course on the belief by consumers that anybody not getting certified is of quality 0, a belief that is confirmed in equilibrium.

For more on this, see Lizzeri (1999).


Certification (6)


111

In actuality, indeed, certification is often remarkably undifferentiated among products: either you get certified or you don’t (Organic, Fair Trade, Verisign for payment over the Internet).

You are never going to be told: this bread is 50% organic, for example.

Your university degree is a certificate with several certification intervals: 1, 2(1), 2(2), ...

Spence’s job market signaling (1)


112

This model does not assume that students learn anything in school or that good results are any indication of future productivity in the labor market.

Instead, this model will only assume that the most productive people suffer less in the educational system than less productive people. Then, one may have equilibria where the most productive go through education only to differentiate from others.

The employers use the education system as a screening mechanism.



113

Two types of students, H and L, with high and low productivity respectively. Production made with type H is 60 and with type L is 40.

Proportion p of students are H. Grade e∈[0,100], costs effort e/60 for students of

type L and e/40 for students of type H. Suppose all students choose to get the same grade

e. Then the firm cannot choose between students, so expected productivity is p*60+(1-p)*40.



114

If students can negotiate wages, then they ask to be paid their expected productivity, so w= p*60+(1-p)*40.

A student who choose another effort level e’ is identified as her being of type L.

The best deviation is then e’=0. The equilibrium is sustained if 40<w-e/40 and 40<w-e/60,

i.e. if e<p*20*40. The required education level must not be too high. The best

is actually to set e=0. The equilibrium is based on unreasonable beliefs as for

example e’>e must be interpreted as coming from a low type.



115

Consider thus another equilibrium such that type H chooses education f (for first) and type L chooses education s (for second).

Suppose education f is rewarded with wage 60 and education s is rewarded with wage 40.

This is sustained if type H gets education f and type L gets education s.

I must thus have 60-f/60>40-s/60 (type h prefers education f) and 40-s/40>60-f/40 (type l prefers education s).

I must also have 60-f/60>0 and 40-s/40>0.



116

Note there is no point for L to get any education, so s=0.

H will get education only in so far as to not be imitated by L, so 40=60-f/40, so f=20*40.

Some education is thus necessary. The low type loses out compared to the pooling equilibrium, the high type gains from it if p*60+(1-p)*40<60-20*40/60, that is if 1-p>2/3, i.e. p<1/3.

Only if type H are sufficiently rare will they prefer to differentiate rather than stay in the mould with others.



117

From a practical view point, an economy that does not require specialized rare skills where differences between individual abilities can emerge, will not want to provide differentiated education levels, but rather the basics for all and not more, e.g. China, France in the 19th century.

An economy that is based on creative industries and rewards individual performances will see the emergence of competitive and differentiated education systems to allow ability signaling.

For more on this, see Aghion-Howitt (2006), which links macroeconomic growth with the micro-structure of education.

http://www.mitpressjournals.org/doi/abs/10.1162/jeea.2006.4.2-3.269�


Asymmetric information

Adverse selection ‘Lemons’ markets Market unravelling Beliefs Signalling Screening Reputation.

118


References (week 4)


119

Textbook readings: Kreps, ch. 17 Holt, ch. 10

Essential readings: Akerlof G. (1970): “The Market for Lemons: Quality

Uncertainty and the Market Mechanism”, Quarterly Journal of Economics, Vol. 84(3), pp.488-500

Spence A. (1973): “Job Market Signaling”, Quarterly Journal of Economics, Vol 87, pp. 355-374.




Optional readings


120

Dellarocas C. (2006): "Strategic Manipulation of Internet Opinion Forums: Implications for Consumers and Firms", Management Science, 52(10), pp. 1577-1593

Hall G. (1977): "Guarantees and Risk-Sharing", The Review of Economic Studies, 44(3), pp. 549-560.

Lizzeri A. (1999): "Information Revelation and Certification Intermediaries", The RAND Journal of Economics, 30(2), pp. 214-231

Miller R.M. and C.R. Plott (1985): “Product Quality Signaling in Experimental Markets”, Econometrica, Vol. 53, pp. 837-872.

Nelson P. (1974): "Advertising as Information", The Journal of Political Economy, 82(4), pp. 729-754

Aghion P. and P. Howitt (2006): "Appropriate Growth Policy: A Unifying Framework", Journal of the European Economic Association, 4(2-3), pp. 269-314. (An interesting reference linking education policy and growth.)










A model of the labour marketThe fair wage hypothesis and its consequenceHow is trust created and maintained?

Week 5: Moral hazard, trust and the labour market

121


A model of the labour market (1)


122

One employer offers wage w to one worker. If the worker accepts the wage, then she is asked to

exert effort e in her job. This effort e cannot be monitored (incomplete contract). Profit for the firm increases in the effort of the

employee, e.g. profit=A+p*e-w, with p the productivity of effort and A the baseline profit.

Effort is costly to the employee, so her net utility is U=w-c*e-B, with c the marginal cost of effort and B the reservation wage (i.e. the wage cannot be less than B).

A model of the labour market (2)


123

This game presents conflicting incentives, which is necessary for it to be interesting!

The Nash equilibrium is such that for any wage w offered by the firm, the employee does zero effort.

Knowing this, the firm offers wage B. The firm’s profit is then A-B. If this is negative, then there

is no production and no employment in equilibrium. By backward induction, this holds in a repeated version

of this game, i.e. if the firm and the employer are in a long term relation.

The fair wage hypothesis


124

In experiments, in the same game, firms offer wages above zero and workers make effort.

Moreover, the higher the wage, the higher is the effort provided.

Lowering effort is punished with lower wages. This is actually all the more true the more productivity

depends on effort: firms will offer higher wages than what most workers ask for!

Firms that choose to punish workers who shirk (do less effort than expected) then fail to elicit higher effort with higher wages (lack of trust).

Fehr et alii (1993)


125



Fehr and Falk (1999)


126

In the article above, a modified labour market is considered:

Double-auction, where workers each say what wage they are ready to accept (wage bid), and firms say what wage they are willing to pay (wage offer).

Workers then choose which firm to work for and firms choose which worker to hire.

The following graphs show the range of wage bids and the hiring wage in two settings: In the first, p and c both equal 0. In the second, p and c are both more than 0.



Fehr and Falk (1999)


127

‘No effort’ treatmentReservation wage=20

‘Effort’ treatmentReservation wage=20

Fehr and Gachter (2000)


128

In this modified labour market setting, firms can punish workers who ‘shirk’, i.e. do less effort than expected.

This punishment is wasteful, i.e. it costs the firm the same amount it withdraws from employees. If the firm chooses to punish the worker by x, then its profit is A+p*e-w-x and utility for the worker is U=w-c*e-B-x

Note that x comes as a negative value in both expressions.

The following graph compares effort induced if the firm chooses to punish employees and if it does not.



Fehr and Gachter (2000)


129

Fehr et alii (2007)


130

In the experiment in the article above, instead of punishing, the firms can choose to give bonuses to employees after effort is revealed.

To the difference of punishments, those bonuses are not wasteful, they are simply a transfer from the firm to the employee, so if the firm chooses to give bonus b to the worker, then its profit is A+d*e-w-b and utility for the worker is U=w-c*e-B+b.

3 treatments: trust contract (no incentives, positive or negative), incentive contract (punishment), bonus contract.

http://www.blackwell-synergy.com/doi/abs/10.1111/j.1468-0262.2007.00734.x�

http://www.blackwell-synergy.com/doi/abs/10.1111/j.1468-0262.2007.00734.x�

Fehr et alii (2007)


131

Treatment 1: Choice between incentive and trust contracts: When given the choice between incentive contracts and trust contracts, firms prefer incentive contracts, even though those do not induce much higher effort and profit was the same. The firms chose to impose the maximum fine in case of lower effort than asked (note: probability of detection=1/3).

Fehr et alii (2007)


132

Treatment 2: Choice between bonus and incentive contracts: When given the choice between bonus contracts and incentive contracts, firms prefer bonus contracts, and those induce much higher effort and much higher profits than incentive contracts. Bonuses paid were about half of wages ON AVERAGE but are highly dependent on effort made.

Fehr et alii (2007)


133

In conclusion, fairness considerations are very important in the use of incentive contracts and firms are mindful of this as they are able to choose those types of contracts that perform best.

In practice, performance related bonuses are seldom used, and when used, are weakly correlated with actual performance...

This may be due to the complexity of the objectives required of workers. Their results are difficult to measure, and rewards based on one measure only can have perverse effects (e.g. stock prices, sales)

Macroeconomic consequences


134

The fair wage hypothesis means that firms will pay workers above ‘market’ wages (i.e. the lowest amount they would be prepared to accept).

This means there is unemployment in equilibrium: firms hire less workers than the market is ready to provide.

Note this is NOT due to workers’ reluctance to accept lower wages, but to firms’ reluctance to lower their wages.

This ties in with Keynes and his ‘sticky wages’ unemployment theory (see also Akerlof-Yellen, 1990)

http://links.jstor.org/sici?sici=0033-5533(199005)105:2<255:TFWHAU>2.0.CO;2-Q�

A basic trust game (1)


135

In the following, we explore further what leads to trust being given or received (i.e. not only in an employment relationship)

The Nash equilibrium of the game below is (Withhold, Violate). However, in practice, a fair amount of trust is offered and fulfilled in this game.

Trustee

Fulfil Violate

Truster Trust 6,6 -6,9

Withhold 0,0 0,0

A basic trust game (2)


136

-6 is the trustee’s exposure in case trust is violated. +6 is the trustee’s gain in case trust is fulfilled. 9-6=3 is the trustee’s temptation to violate trust. Both truster and trustee gain if trust is maintained:

mutual gain.

Bacharach et alii (2007)

There are several variants on the basic trust game, where truster only

gains (A) where both truster and

trustee gain the same (B)

where truster gains more than trustee (C)

137


Fulfil Violate

Trust 6,6 -6,9

Withhold 0,6 0,6

Fulfil Violate

Trust 6,6 -6,9

Withhold 0,0 0,0

Fulfil Violate

Trust 6,6 -6,9

Withhold -3,0 -3,0

(A)

(B)

(C)

Increase in trusting and fulfilment

http://www.springerlink.com/content/8gm68l3375094538/�


Bacharach et alii (2007)


138

Trustworthiness: the truster is more likely to trust if she expects trust to be fulfilled.

Trust responsiveness: trust fulfilling increases as the trustee believes the truster trusts him. As seen before, trust may not be enhanced by the threat of

punishment if trust is not fulfilled.

Trust responsiveness will be affected by the incentive for the truster to obtain trust. Trust is not necessarily enhanced in a repeated game setting:

‘trust is its own reward’...

Trust is enhanced by belonging to the same ‘group’, though distrust emerges when dealing with another ‘group’...




Moral hazard Trust Efficiency wage Complete and

incomplete contracts

139


References (week 5)

Textbook readings: Kreps, ch. 16 Holt, Ch. 13

Essential readings: Akerlof G.A. and J.L. Yellen (1990): "The Fair Wage-Effort Hypothesis

and Unemployment", The Quarterly Journal of Economics, 105(2), pp. 255-283.

Camerer C. (2003): “Behavioural Game Theory: Experiments in Strategic Interaction”, section 2.7.

Fehr, E. and S. Gachter (2000): “Fairness and Retaliation: The Economics of Reciprocity”, Journal of Economic Perspectives 14, pp. 159-181. Also available on the web as University of Zurich Institute of Empirical

Research in Economics Working Paper No. 40 at http://www.iew.unizh.ch/wp/iewwp040.pdf


140





http://www.iew.unizh.ch/wp/iewwp040.pdf�

Optional readings

Fehr E. and A. Falk (1999): “Wage Rigidity in a Competitive Incomplete Contract Market”, Journal of Political Economy, 107(1), pp. 106-134.

Fehr E., Kirchsteiger G. and A. Riedl (1993): "Does Fairness Prevent Market Clearing? An Experimental Investigation", The Quarterly Journal of Economics, 108(2), pp. 437-459.

Fehr E., Klein A. and K.M. Schmidt (2007): “Fairness and Contract Design”, Econometrica 75, pp. 121-154.

Milgrom P. and J. Roberts (1992): “Economics, Organization and Management”, Prentice-Hall, ch. 7, pp. 214-236. A more advanced treatment of moral hazard.


141







Wrapping up (1)


142

What did we learn? Aversion to losses, regrets and ambiguity and other

patterns in choice behavior. The meaning of rationality and some instances and

rationalizations of irrational behavior. The unravelling of markets with asymmetric information

and how to foster market efficiency. The determinants of trust and other exceptions to self-

interested behavior

Wrapping up (2)


143

A number of micro-economic principles are used in macro theory: Fairness → rigidities in the labour market. Irrational exuberance → extreme market fluctuations. The micro-structure of market → efficiency properties

of the market institutions. Moral hazard and adverse selection → insurance and

investment behavior. Anomalies in consumer choices → should they be

corrected or accepted as the outcome of utility maximization?

Alexia GaudeulSpring 2009


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