Lesson overview
Chapter 10 Strategic Moves
Lesson II.6 Strategic Move Theory
Each Example Game Introduces some Game Theory
• Example 1: Unconditional Strategic Moves
• Example 2: Credibility
• Example 3: Implicit Promises
• Example 4: Delegation
• Example 5: Brinksmanship
• Example 6: Threats verses Promises
Lesson II.7 Strategic Move Applications
BA 592 Lesson II.6 Strategic Move Theory
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Example 1: Unconditional Strategic Moves
A game specifies the choices or moves available to the players,
the order, if any, of those moves, and the payoffs resulting from
all logically possible combinations of all the players’ choices.
Equilibrium outcomes are typically affected by changing any one
of those features --- adding or removing available moves,
changing the order or removing order an making a game
simultaneous, or changing payoffs. Hence, each player has an
incentive to manipulate the game specifications to produce an
outcome more to his advantage. Strategic moves are devices to
manipulate games.
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Example 1: Unconditional Strategic Moves
The simplest way to change a game is to move first. But, what
does it mean to “move first”?
First, your actions must be observable to the other player.
Second, they must be irreversible.
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Example 1: Unconditional Strategic Moves
Emily
Contribute
Don't
Nina
Nina
Contribute
Don't
Contribute
Don't
Talia
Talia
Talia
Talia
Cont.
Don't
Cont.
Don't
Cont.
Don't
Cont.
Don't
3.5,3.5,3.5
3,3,4
3,4,3
1,2,2
4,3,3
2,1,2
2,2,1
0,0,0
The Street Garden Game tree to
the upper left has a unique
rollback equilibrium, with only
Nina and Talia contributing and
getting payoff 3.
Emily
Contribute
Don't
Nina
Nina
Don't
Don't
Talia
Talia
Cont.
Don't
Cont.
Don't
3,4,3
1,2,2
2,2,1
0,0,0
Nina gets payoff 4 if she
commits to not contributing,
say by putting all her money
into an alternative project. That
removes Contribute from her
available moves, and changes
the rollback equilibrium of the
tree on the lower left.
BA 592 Lesson I.3 Sequential Move Theory
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Example 2: Conditional Strategic Moves
Conditional strategic moves are another way for Player A to
change a game with Player B. Declare in the first stage: “In the
following game, If you choose X1, I will choose Y1; if you
choose X2, I will choose Y2 ; … . In other words Player A can
commit to a response rule. One requirement is Player A has to be
physically able to wait to make his move at the second stage until
he has observed what Player B has irreversibly done.
Conditional strategic moves can deter Player B from making a
certain move or can compel Player B to make a move. The
actions taken by Player A can be negative threats or positive
promises.
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Example 2: Conditional Strategic Moves
Parents constantly try to influence the behavior of their children
by using threats and promises. And children know well that
many of these threats and promises are not credible. Much bad
behavior can escape the threatened punishment if the child
sweetly promises not to do that again, even though the child’s
promise itself may not be credible.
Determine the decision tree where the Child decides whether to
eat his vegetables. (It is a decision tree since there is only one
player.)
Then change that tree into a game tree where a Parent first might
threaten a child “no dessert unless you finish your vegetables”
then the Child decides whether to eat his vegetables.
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Example 2: Conditional Strategic Moves
Decision tree without parents:
Child
No Eat
Eat
?
?
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Example 2: Conditional Strategic Moves
“No dessert unless you finish your vegetables” tree:
Parent
No Threat
Threat
Child
Child
No Eat
Eat
No Eat
Eat
Parent
Parent
Parent
Parent
No Des.
Des.
No Des.
Des.
No Des.
Des.
No Des.
Des.
?,?
?,?
?,?
?,?
?,?
?,?
?,?
?,?
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Example 3: Implicit Promises or Threats
Threats by Player A to deter or compel a move by Player B
implicitly imply a promise if Player B as requested. The Parent’s
explicit threat “no dessert unless you finish your vegetables”
implicitly makes the promise “dessert if you finish your
vegetables”. Likewise, the explicit promise “dessert if you finish
your vegetables” implicitly makes the treat “no dessert unless you
finish your vegetables”.
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Example 3: Implicit Promises or Threats
Whether to make a treat or promise explicit, and which can be
left implicit, depends on whether the payoffs to Player A make
the threat or the promise a best response. On the one hand, if a
parent thinks deserts are good for their child, then “no dessert
unless you finish your vegetables” needs to be an explicit threat,
while the promise “dessert if you finish your vegetables” can be
left unsaid. On the other hand, if a parent thinks deserts are bad
for their child, then “dessert if you finish your vegetables” needs
to be an explicit promise, while the treat “no dessert unless you
finish your vegetables” can be left unsaid.
Explicit threats and promises are needed when they are not in
Player A’s best interests to carry out. That is, when the threat
does mutual harm to both players, or when the promise harms A.
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Example 3: Implicit Promises or Threats
Suppose a Child gets -1 happiness from eating his vegetables and
0 from not eating. Determine the decision tree where a Child
decides whether to eat his vegetables. (It is a decision tree since
there is only one player.)
Suppose, regardless of whether the Child eats his vegetables, he
gets +2 additional happiness from eating dessert and 0 from not
eating dessert. Suppose the Parent gets +2 happiness if the Child
eats vegetables and 0 from not eating, and an additional +1
happiness if the child eats dessert and 0 from not eating. Hence,
change the decision tree into a game tree where a Parent first
might threaten a child “no dessert unless you finish your
vegetables” then the Child decides whether to eat his vegetables.
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Example 3: Implicit Promises or Threats
Decision tree without parents:
Child
No Eat
Eat
0
-1
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Example 3: Implicit Promises or Threats
“No dessert unless you finish your vegetables” tree. (Parent
payoff is first, Child second.) Parent
No Threat
Threat
Child
Child
No Eat
Eat
No Eat
Eat
Parent
Parent
Parent
Parent
No Des.
Des.
No Des.
Des.
No Des.
Des.
No Des.
Des.
0,0
2,1
2,-1
3,1
0,0
2,1
2,-1
3,1
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Example 3: Implicit Promises or Threats
Parent
No Threat
Threat
Child
Child
No Eat
Eat
No Eat
Eat
Parent
Parent
Parent
Parent
No Des.
Des.
No Des.
Des.
No Des.
Des.
No Des.
Des.
0,0
1,2
2,-1
3,1
0,0
1,2
2,-1
3,1
Partial rollback solution:
If the Parent makes no threat,
the offers Desert (which the
Child eats) but the Child
refuses vegetables. The Parent
gets payoff 1.
If the Child eats vegetables, the
Parent offers Desert (which the
Child eats). Thus the threat
need not specify “dessert if you
finish your vegetables”.
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Example 3: Implicit Promises or Threats
Parent
No Threat
Threat
Child
Child
No Eat
Eat
No Eat
Eat
Parent
Parent
Parent
Parent
No Des.
Des.
No Des.
Des.
No Des.
No Des.
Des.
0,0
1,2
2,-1
3,1
0,0
2,-1
3,1
Parent
No Threat
Threat
Child
Child
No Eat
Eat
No Eat
Eat
Parent
Parent
Parent
Parent
No Des.
Des.
No Des.
Des.
No Des.
Des.
No Des.
Des.
0,0
1,2
2,-1
3,1
0,0
-1,2
2,-1
3,1
Threat subgame:
The threat can take the form of
removing the option of desert if
the Child does not eat
vegetables, as shown in the tree
on the upper left.
Or, the threat can reduce the
Parent’s payoff (say, wimpy
reputation looses 2 units) if the
Child does not eat vegetables
but does eat desert, as show in
the tree on the lower left.
In either case, the Parent gets 3.
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Example 4: Delegation
Threats can be made credible if Player A turns over their
execution to a third party. Of course, this only solves the
problem for Player A if the third party can credibly carry out both
the threat of punishment for non-compliance by Player B and the
implied promise of non-punishment for compliance by Player B.
On the one hand, if the third party prefers to punish Player B,
then credibility is doubtful for the non-punishment for
compliance by Player B. On the one hand, if the third party
prefers to not punish Player B, then credibility is doubtful for the
punishment for non-compliance by Player B.
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Example 4: Delegation
Trade friction between the U.S. and Japan creates an incentive for
strategic moves. Suppose either country can Open or Close trade
to the other countries imports.
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Example 4: Delegation
For the U.S., the best outcome is Open imports by both countries.
Specifically, suppose the U.S. values Open imports to Japan at 1
(because U.S. producers gain), and the U.S. values Open imports
from Japan at 2 (because U.S. consumers gain more than U.S.
producers loose).
For Japan, the best outcome is Open imports to the U.S. but
Closed imports from the U.S.. Specifically, suppose Japan values
Open imports to the U.S. at 2 (because Japanese producers gain),
and Japan values Closed imports from the U.S. at 1 (because the
Japanese producers’ gain is valued more highly by the Japanese
government than the Japanese consumers’ loss).
Discuss the possibilities and difficulties for strategic moves in
that Trade Relations Game.
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Example 4: Delegation
The U.S. and Japanese strategies and payoffs define a normal
form. The U.S. has a dominate strategy of Open imports, and
Japan has a dominate strategy of Closed imports. That gives
Japan payoff 3, which is the highest possible, but the U.S. gets 2.
Hence, the U.S. has an incentive for a strategic move to cause
both countries to Open imports.
Japan
U.S.
Open
Closed
Open
3,2
1,0
BA 592 Lesson II.6 Strategic Move Theory
Closed
2,3
0,1
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Example 4: Delegation
Japan
U.S.
Open
Closed
Open
3,2
1,0
Closed
2,3
0,1
The U.S. cannot get to its preferred strategies of Open imports by
both countries by an unconditional strategic move to Open
imports since Japan would respond with its dominate strategy of
Closed imports. Can the U.S. get its preferred position with the
threat “We’ll Close imports if you Close imports”?
If that conditional strategic move were credible, Japan’s payoffs
from Open would be 2, and from closed would be 1, so they
would choose Open, giving the U.S. its preferred outcome.
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Example 4: Delegation
Japan
U.S.
Open
Closed
Open
3,2
1,0
Closed
2,3
0,1
The threat “we’ll Close imports if you Close imports” is hard to
make credible since it is not in U.S. interests to Close imports if
Japan has Closed imports. In fact, Closed imports for the U.S. is
a dominated strategy.
One possible solution is to delegate the U.S. response to Japan to
the U.S. Commerce Department, which is a group that values
only U.S. producers, and for which Closed imports is a dominate
strategy. That makes the explicit threat “we’ll Close imports if
you Close imports” credible, but it makes the implied promise
“we’ll Open imports if you Open imports” less credible.
BA 592 Lesson II.6 Strategic Move Theory
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Example 4: Delegation
Japan
U.S.
Open
Closed
Open
3,2
1,0
Closed
2,3
0,1
Putting it all together, delegation alone does not make both the
threat “we’ll Close imports if you Close imports” and the implied
promise credible. A reputation for toughness of the U.S. may
have to decrease U.S. payoffs enough to make Closed imports in
the U.S. be the best response to Closed imports in Japan.
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Example 5: Brinksmanship
Threats are sometimes too large to be credible. “We’ll refuse to
defend you in the future if you Close imports” might be too big to
make credible based on our incentive to have a tough reputation.
One way to scale down the size of such a treat is to make it a risk
but not a certainty: “We are less likely to defend you in the future
if you Close imports”. Threatening with the risk of large
mutually-harmful penalties is called brinksmanship.
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Example 5: Brinksmanship
The chance of things sliding out of control is also often used as a
tool of brinkmanship, because it can provide credibility to an
otherwise incredible threat. For example, Kennedy was not
willing to start a nuclear war over the Cuban Missile Crisis, but
he was willing to take actions that risked the accidental start of a
nuclear war. If Kennedy had said “If you station your warheads
in Cuba, we start a shooting war and exterminate human life on
this planet” nobody would have believed him, but instead
Kennedy ordered a naval quarantine.
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Example 5: Brinksmanship
Until the crisis ended, there was a continual risk of the accidental
outbreak of nuclear war. For example, when an unknown Soviet
anti-aircraft battery commander shot down an American U-2
surveillance plane without authorization. With U.S. forces on
high alert, this single, unauthorized action could have prompted
an attack on the Cuban bases, which might have quickly escalated
into nuclear exchanges. In summary, Kennedy's actions created
an ongoing elevated risk of an accidental nuclear exchange, with
the hope that the Soviets would back down from positioning
missiles in Cuba in order to reduce the risk Kennedy had created.
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Example 6: Threats verses Promises
Threats and Promises by Player A are both costly if they actually
occur, but if they are successful in changing the beliefs, and so
the behavior, of Player B, the threat need not be carried out but
the promise must be carried out. This has two implications:
First, promises should be kept to the minimum to cause the
desired change while threats can be bigger than the minimum, so
long as the threat does not become incredibly big “Do that again
and I’ll kill you!”.
Second, threats are cheaper to Player A than promises.
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Example 6: Threats verses Promises
Suppose a Child looses 1 happiness from studying so hard he gets
a B average. Determine the decision tree where a Child decides
whether to study to get a B average. (It is a decision tree since
there is only one player.)
BA 592 Lesson II.6 Strategic Move Theory
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Example 6: Threats verses Promises
Decision tree without parents:
Child
No Study
Study
0
-1
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Example 6: Threats verses Promises
Suppose, regardless of whether the Child gets a B average, he
would loose 2 happiness if he were grounded at home for a
month, and he would get +2 additional happiness if given a new
bike.
Suppose the Parent would get +2 happiness if the Child gets a B
average, the Parent would loose 1 happiness if he grounds the
child, and the Parent would loose 1 happiness if the Parent gives
the Child a new bike (That 1 happiness lost is the sum total of the
Parents value of the child getting the bike minus the purchase
price.)
Hence, change the decision tree into a game tree and decide
whether it is better for the parent to threaten or promise.
BA 592 Lesson II.6 Strategic Move Theory
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Example 6: Threats verses Promises
“You’re grounded if you get less than a B average” threat tree:
Suppose the Parent manages to
impose a cost of C units of
happiness if he does not carry
through on the threat.
Parent
No Threat
Threat
Child
Child
No Study
Study
No Study
Study
Parent
Parent
Parent
Parent
No Gr.
Ground
No Gr.
Ground
No Gr.
Ground
No Gr.
Ground
0,0
-1,-2
2,-1
1,-3
-C,0
-1,-2
2,-1
1,-3
For any C > 0, partial rollback
of the tree indicates that, if not
threatened, the Child will not
study, and the Parent earns
payoff 0. (The Parent’s payoff
number is the first one.)
BA 592 Lesson II.6 Strategic Move Theory
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Example 6: Threats verses Promises
“You’re grounded if you get less than a B average” threat tree:
For any C > 1, complete
rollback of the tree indicates
that the Child will study, and
the Parent will not ground the
child, and the Parent earns
payoff 2. (The Parent’s payoff
number is the first one.)
Parent
No Threat
Threat
Child
Child
No Study
Study
No Study
Study
Parent
Parent
Parent
Parent
No Gr.
Ground
No Gr.
Ground
No Gr.
Ground
No Gr.
Ground
0,0
-1,-2
2,-1
1,-3
-C,0
-1,-2
2,-1
1,-3
BA 592 Lesson II.6 Strategic Move Theory
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Example 6: Threats verses Promises
“You get a bike if you get a B average” promise tree:
Suppose the Parent manages to
impose a cost of C units of
happiness if he does not carry
through on the promise.
Parent
No Prom.
Promise
Child
Child
No Study
Study
No Study
Study
Parent
Parent
Parent
Parent
No Bik.
Bike
No Bik.
Bike
No Bik.
Bike
No Bik.
Bike
0,0
-1,2
2,-1
1,1
0,0
-1,2
2-C,-1
1,1
For any C > 0, partial rollback
of the tree indicates that, if
promised a bike, the Child will
not study, and the Parent earns
payoff 0. (The Parent’s payoff
number is the first one.)
BA 592 Lesson II.6 Strategic Move Theory
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Example 6: Threats verses Promises
“You get a bike if you get a B average” promise tree:
For any C > 1, complete
rollback of the tree indicates
that the Child will study, and
the Parent will give the bike to
the child, and the Parent earns
payoff 1. (The Parent’s payoff
number is the first one.)
Parent
No Prom.
Promise
Child
Child
No Study
Study
No Study
Study
Parent
Parent
Parent
Parent
No Bik.
Bike
No Bik.
Bike
No Bik.
Bike
No Bik.
Bike
0,0
-1,2
2,-1
1,1
0,0
-1,2
2-C,-1
1,1
BA 592 Lesson II.6 Strategic Move Theory
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Example 6: Threats verses Promises
Putting it all together, the threat “You’re grounded if you get less
than a B average” earns the Parent payoff 2 (and the threat is not
carried out in equilibrium), which is better for the Parent than the
payoff 1 from the promise “You get a bike if you get a B
average”, which is better for the Parent than the payoff 0 from not
threatening and not promising.
BA 592 Lesson II.6 Strategic Move Theory
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BA 592
Game Theory
End of Lesson II.6
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