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LECTURE #4
19 January 2006
Copyright: Ronald B. Mitchell, 2006
IMPORTANT: The
notation OR: in the syllabus means that the reading is an "Online
Reading," not that the reading is not required.
I. Intro
II. Problem Structures: Thinking about Incentives in Game Theory terms
A. This is another way to help you think about the stuff we discussed in
previous class
B. Games Notation:
1. CELLS contain 2 Payoffs, i.e., the value of a particular outcome to
that player, with payoffs being potentially different for each player -
right hand number is always Col's payoff and left hand is always Row's
payoff
2. Columns and rows contain Strategies of one player
3. Rs-s is the payoff to player R (for "Row") of the outcome
produced when Row plays S and Col also plays S
4. Cns-s (right side of bottom left cell) is the payoff to player C
(for "Col") of the outcome produced when Row plays not-S but Col
plays S
5. Numbers arranged so that higher the payoff number, the better or
more preferred that is
6. Games are simplified as two players but can usually have multiple
players
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C(ol) plays Strategy S |
C(ol) plays Strategy of not-S |
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R(ow) plays Strategy S |
Rs-s, Cs-s |
Rs-ns, Cs-ns |
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R(ow) plays: Strategy of not-S |
Rns-s, Cns-s |
Rns-ns, Cns-ns |
C. Harmony - no conflict situation where independent
decisions lead to outcomes preferred by all parties. Preferences are
independent or mutually beneficial.
1. No institution needed to resolve conflict because there is no
conflict
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Allow education of foreigners in your universities |
Do not allow education of foreigners in your
universities |
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Allow education of foreigners in your universities |
4,4 |
3,2 |
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Do not allow education of foreigners in your
universities |
2,3 |
1,1 |
D. Deadlock – most basic and unrepentant form of
conflict. No middle ground. Interests are diametrically opposed. Zero sum
conflicts.
1. Both sides have an unambiguously preferred strategy which involves
harming the other side.
2. Although both sides preferred OUTCOME (the cell) is the other side
stopping from engaging in the conflict while they continue (i.e., kill
them without being killed in exchange), if they can't have that, they
prefer continuing the conflict over halting it
3. Although Deadlock can become another game over time, and then may
be subject to cooperation, so long as preferences are truly Deadlock
preferences, there is no resolution
4. Examples: ancient hatreds, ethnic violence, conflicts over values
(e.g., whaling?)
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Stop engaging in conflict |
Continue engaging in conflict |
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Stop engaging in conflict |
2,2 |
1,4 |
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Continue engaging in conflict |
4,1 |
3,3 |
E. Positive externalities plagued by incapacity – hard
because incentives on one side to remedy may not be sufficient to generate
solution to the problem because of incapacity.
1. Problem is one of incapacity not incentives
2. All states better off if they cooperate in addressing the problem
but some states simply don't have the capacity
3. States that do have the capacity must have sufficient interest to
pay for others to contribute - capable have to "foot the bill"
for the incapable
4. Examples: health care, particularly AIDS – all have incentives
to prevent but nobody wants to pay.
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Incapable state ==>
Capable state --vvv-- |
Contribute to AIDS prevention (but NOT POSSIBLE) |
Don't contribute to AIDS prevention |
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Contribute to AIDS prevention |
3,4 |
2,3 |
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Don't contribute to AIDS prevention |
4,2 |
1,1 |
F. Upstream/downstream problem - similar to suasion
1. Upstream states receive no direct benefits from cooperation and
probably incurs costs to cooperate. Willing to cooperate only if receive
sidepayments that outweigh these costs
2. Very strong incentives for upstream states to renege on their
commitments after agreement is reached - problems of obsolescing
bargains
3. Example: French reduction of pollution of the Rhine river,
Canadian control of dams on the Columbia; nuclear weapons programs of
weak (as "upstream") states
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Upstream state ==>
Downstream state --vvv-- |
Contribute to pollution reduction |
Don't contribute to pollution reduction |
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Contribute to pollution reduction |
4,1 |
2,3 |
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Don't contribute to pollution reduction |
3,1 |
1,3 |
G. Coordination (Battle of the Sexes) – easy because all
states have incentives to agree and once states agree on how to cooperate,
there are no incentives to defect. Example: English as common language for
airline pilots and air traffic controllers; international ship navigation
rules (sail on the right side of a sea-lane); assignment of domain names to
avoid conflicts
1. Two possible equilibriums, one of which benefits one side and one
of which benefits the other but where both prefer cooperation to
non-cooperation
2. Examples: satellite slot allocations, navigation rights, language
for air traffic controllers, URLs for websites
3. This is what Stein calls "Dilemma of common aversion and
divergent interests" or Battle of the Sexes in Krasner
4. Krasner makes point that how one resolves these problems depends
on whether power is symmetric among actors or unbalanced.
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Train pilots in Row Language |
Train pilots in Col Language |
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Train pilots in Row Language |
4,3 |
1,2 |
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Train pilots in Col Language |
2,1 |
3,4 |
H. Suasion problems – really hard because some states
have no incentives to agree and even if they do agree, they still have
incentives and ability to defect.
1. Both strong and weak states benefit from cooperation but strong
state is willing to provide all of the benefits without help but prefers
that weaker states contribute
2. Weaker states have "a strong incentive to free-ride, knowing
that public goods… will nevertheless be provided" [Martin, 1992
#1964].
3. Example: burden sharing with respect to security in Europe during
Cold War (or, arguably, burden sharing for Iraq war)
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Weak state ==>
Strong state --vvv-- |
Contribute to defense or pollution reduction |
Don't contribute to defense or pollution reduction |
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Contribute to defense or pollution reduction |
4,3 |
3,4 |
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Don't contribute to defense or pollution reduction |
2,2 |
1,1 |
I. Collaboration (Prisoners' Dilemma) – hard because
although all states have incentives to agree, even after states agree on how
to cooperate, there are still strong incentives to defect. Standard
Prisoners’ Dilemma (PD) or Tragedy of the Commons.
1. There are costs to both (or all) players of cooperating and the
value of cooperating depends on all others contributing, so it makes
little sense to contribute if nobody else does (since the goal won't be
accomplished, but it also makes little sense to contribute if everybody
else does (since the goal will be accomplished even if you don't
contribute and you can save the cost of compliance)
2. Both (or all) sides in the problem prefer mutual cooperation to
mutual cheating but both prefer even more their own unilateral cheating
3. Game assumes symmetry in the positions of the actors - both are
assumed as polluters, which may not always be the case
4. Examples: arms races, trade wars, OPEC price setting, many
environmental problems particularly overharvest of a resource (e.g.,
fish, fur seals)
5. Known as Tragedy of the Commons in environmental issues
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Stop polluting |
Continue polluting |
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Stop polluting |
3,3 |
1,4 |
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Continue polluting |
4,1 |
2,2 |
J. Assurance problems - All states want to collaborate and
believe they will be better off if they do, but they lack perfect
information and so may fail to coordinate their behavior by accident and
because of excessive lack of trust.
1. Problem is one of imperfect information, not one of incentives
2. War games and pre-announcing them. Each country wants to make sure
that other state knows it is only doing a war game and not actually
attacking.
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Announce war game |
Don't announce war game |
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Announce war game |
4,4 |
1,3 |
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Don't announce war game |
3,1 |
2,2 |
K. Capacity, knowledge and norms problems are not well-suited for placing
in game theoretic terms but doesn't mean they aren't important. Just can't
fit them readily into these sorts of intellectual matrices.
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