Global Tragedies: Essential Models

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Global TragediesEssential Models

• Richard Cornes
• Professor of Economic Theory
• P.O.E.T.

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The Economists Mantra
Let us assume
Why?
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Noneconomists tend to be too academic. They
abstract too much from the real world.
Ian Little Lloyds Bank Review, 1957
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Why we need economic models

• We cannot avoid them.
• The choice is between explicit conscious and
  implicit unconscious modelling.
• A model that is too complicated is useless
• Jorge Luis Borges

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Two Pitfalls of Implicit Modelling(I) The False
Analogy
(i) Employees are like nails. Just as nails must
be hit on the head in order to make them work,
so must employees. (ii) Countries are like
firms. Just like firms, their survival depends
on their producing goods at lower costs than
their rivals.
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II Fallacy of Composition
(i) "I can see the concert better by standing on
my seat. Therefore, if everybody stood on their
seats, we would all see better." (ii) "A person
who pursues his best interests at the expense of
others is better off than one who does not.
Therefore, if everybody pursued a policy of
their own interests at the expense of others, we
would all be better off."
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The real issues

• How far should we go in simplifying?
• Make it as simple as possible,
• but no simpler Einstein
• What simplifications to make?
• The question of style

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A Model (1926)
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Model Mk2 (1932)
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Model Mk3 (1933)
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Model Mk4 (1990s)
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Characteristics of London Underground diagram

• It abstracts
• It distorts
• It is simple, appears natural
• But its development was painstaking
• And it sometime misleads

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The Style of Economics two controversial features

• General preference for analytical reasoning
• over numerical computations.
• Widespread use of the assumption of
• rational economic man.

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The subject matter of Economics
Interacting decision-makers Anns best decision,
and wellbeing, depend on the choice made by
Bruce. Bruces best decision, and wellbeing,
depend on the choice made by Ann.
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Nash and Interactive Choices
John Nash suggested concentrating on the
conditions that must be satisfied by a set of
actions if they are to be acceptable as an
equilibrium set. A Nash equilibrium is a set
of actions, one for each player, such that each
is a best response for that player to the
actions chosen by the others.
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A Famous Game
Colin
Confess
Deny
Rowena
Deportation to Australia
6 months gaol
Confess
6 months gaol
Freedom
10 fine
Freedom
Deny
Deportation to Australia
10 fine
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Three Economic Tragedies

• The tragedy of public good underprovision
• The tragedy of the commons
• The tragedy of the anticommons

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The First TragedyTragedy of the Public
GoodThe parable of Gloom Hall
200 students live in Gloom Hall. Each may
contribute either 10, or zero, towards
lights. A 10 contribution buys extra lighting
that each student values at 10p, or 0.1.
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A Very Few Examples of Public Goods
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A Very Few Examples of Public Goods

• Deterrence
• Financial accounting standards
• Watershed management
• Malaria cure
• Curbing global warming
• Limiting ozone depletion
• Surveillance of borders
• Pest control

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A Very Few Examples of Public Goods

• Deterrence
• Financial accounting standards
• Watershed management
• Malaria cure
• Curbing global warming
• Limiting ozone depletion
• Surveillance of borders
• Pest control

• Immunizing populations
• Curbing organized crime
• Limiting contagions
• Peacekeeping
• Reducing acid rain
• Protection of rainforests
• combating terrorism
• agricultural/genetic research

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The Second TragedyTragedy of the CommonsThe
parable of Smoggville

• Smoggville has 1,000,000 inhabitants.
• A cosy coal fire costs 1.
• A warm fire is worth up to 2.
• Coal inflicts pollution cost of 0.00001
• per person (Laundry bills, health expenses,
  smell, etc.)
• For 1.50, a smokeless fuel is available.

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The Great 1952 London Smog December
4 - December 9 Death toll 4,000 - 12,000
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Examples of Commons
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The Third Tragedy Tragedy of the Anticommons
Each of several players has the right to exclude
others. Imagine a car park where, to acquire
the right to park your car, you must buy a
ticket from each of several firms.
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Examples of Anticommons

• The shopfronts of Moscow
• The rebuilding of Kobe
• Vetoes NATO, EC
• Patent laws
• Especially genetic research,
• and computing technology

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Limitations of the models

• Binary choice - need to have more options
• Very simple technologies
• Homogeneous populations of individuals -
• need to allow for differences.

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Beyond Binary Choice
Can add more alternative actions. This appears
to complicate matters. Paradoxically, it can be
simpler to go all the way, allowing each player
an infinite set of choices
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Public Good Technologies

• Summation
• Weakest link
• Best shot
• Weaker link
• Better shot

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Examples of Technologies
Summation Air pollution control,
desertification, public health infrastructure,
rainforest preservation, satellite communication
network. Weaker link Pest and weed control,
disease surveillance, transportation network,
Basle Banking Accord Better shot Cure of
orphan diseases, monitoring technology eg.
for ozone depletion, deforestation, research.
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Coping with Heterogeneity
... the effective analytic solution of a large
number of even linear equations, is ... not
routine when the number of variables is large.
...this may be subsumed under the heading "the
curse of dimensionality." ... the Scientist,
like the Pilgrim, must wend a straight and
narrow path between the Pitfalls of
Oversimplification and the Morass of
Overcomplication. Bellman, R. (1957), Dynamic
programming
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More general models 2 players
Output of Coca Cola
qcc F(qpc)
qpc F(qcc)
Nash equilibrium
Output of Pepsi Cola
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More general models 3 players
Coca Cola
Nash equilibrium
Novelty Cola
qc F(qp,qn)
qp G(qc,qn)
qn H(qc,qp)
Pepsi Cola
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More general models 4 players
?????????? !!!!!!!!!!!!! ?????????? !!!!!!!!!!!!!
qc F(qp, qn, qm)
qp G(qc, qn, qm)
qn H(qc, qp, qm)
qm H(qc, qp, qn)
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An alternative approach
In our 4-player example, let qA qB qC qC
Q We use replacement functions qA rA(Q), qB
rB(Q) This approach leads to a simple diagram
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The diagram
Replacement values
Nash equilibrium
rD(Q)
rC(Q)
rB(Q)
rA(Q)
Q
45o
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Cost and Output Sharing

• Exogenous sharing rules - formally
• identical to public good problem.
• Proportional sharing rules formally
• identical to tragedy of the commons.
• Suggestion - why not mix the rules?
• Share some part of output exogenously,
• and some part in proportion to
• effort supplied.

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Back to public goods questions addressed by the
model

• Patterns of existing contributions NATO
• Changes in those patterns over time
• Why have Chinese SOEs not done well?
• Who bears greater share of
• global public good provision?
• What incentives exist for improving
• ones unit cost as a public good provider?

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More questions

• Why do some international treaties
• seem successfulMontreal,
• others not Kyoto?
• Why more interest in peacekeeping in
• recent years - what countries will be
• the major peacekeepers?
• How to strengthen incentives to provide aid
• to improve health, and control epidemics?
• HIV/AIDS, SARS

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Last word on Economic Tragedies
END