11: Brinkmanship

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11 Brinkmanship The Tragic Tale of George and
Saddam
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Brinkmanship

• This is an important mechanism for making
  incredible threats credible.
• A threat is a way of making a strategic move.
• But often you only have one large threat
  available. This threat is incredible because if
  its size, your opponent doesnt believe you will
  carry it out.
• Give me five dollars or I will kill myself, may
  not involve a credible threat.
• Give my five dollars or I will run across this
  road with my eyes closed, may be credible and
  thus gain the five dollars.
• The second threat works because you are only
  threatening to kill yourself with a given
  probability (that of being hit by a vehicle). The
  scale of the threat is reduced and thus becomes
  credible.

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Brinkmanship

• One of the most important elements of
  brinkmanship is that the process must be somewhat
  out of control.
• In the running across the road example, if the
  threatener could listen or look to see if a
  vehicle were coming then choose the probability
  of death by deciding when to run.
• But then the threat wouldnt work because all
  parties would know the threatener wouldnt run if
  there were a vehicle coming. They would choose
  the probability zero. Hence the probability of
  the threat actually being carried out must be
  somewhat outside the threateners control.

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The Happy Tale of John and Nikita.

• A striking example of successful brinkmanship was
  the Cuban missile crisis.

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The Happy Tale of John and Nikita.

• The Cuban Missile Crisis was an Example of
  Success of the Brinkmanship Strategy.
• JFK took the world to the brink of nuclear war
  and by doing so persuaded Khrushchev to remove
  missiles from Cuba.
• But it seems as if game theory cannot explain
  this. Why didnt Khrushchev apply backwards
  induction, figure out the final outcome, and
  decide not to start the whole process?
• More to come.obviously.

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The Tragic Tale of George and Saddam

• JFK threatened Khrushchev and forced his
  compliance. Few shots were fired and there was no
  nuclear war.
• He gambled and won.
• GWB played a similar strategy against Saddam
  Hussein gambled and lost. He lost because the
  best outcome was the compliance or removal of
  Saddam simply as a response to Bushs threat. The
  actual outcome was the removal of Saddam but only
  after a costly war.
• Yet Bush and Kennedy played essentially the same
  strategy of brinkmanship.
• Here we might ask why Saddam didnt employ
  backwards induction and quit before the war?

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The Tragic Tale of George and Saddam

• We cannot say GWB in any sense played the game
  better or worse than JFK.
• Brinkmanship necessarily involves taking risks.
  There is a chance of success and failure.
• Something went wrong in the Persian gulf that
  didnt in the Cuban missile crisis, but what was
  it?

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A Simple Threat Model

• Suppose GWB and SH each have two strategies
• GWB - Threaten or Dont.
• SH Quit or Stay.
• A simple threat game then looks as follows

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A Simple Threat Model

• The problem with the simple threat model is that
  backwards induction tells us GWB will always
  threaten and SH will always quitbut this didnt
  happen!! Saddam didnt quit.
• Why?
• Perhaps we have the payoffs wrong.
• Perhaps Saddam values defying the US and simply
  prefers not to quit.
• This suggests the problem is that Saddams
  payoffs differ from those in the game above.

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Another Simple Threat Model.

• Here we see Saddam prefers to stay rather than
  quit.
• But this explanation of events doesnt work
  either. GWB should apply backwards induction and
  choose Dont.

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Applying Brinkmanship

• Two elements are missing in our analysis of the
  tale of George and Saddam.
• GWB didnt know SHs payoffs, were they as in
  threat game 1 or 2? How valuable to SH it was to
  be seen defying the US is not easily known.
• SH nor GWB was sure GWB would invade. There were
  many imponderables including opposition to Bushs
  plans in the UN by France, Germany and Russia.
  But how much of a check there was on Bushs
  actions was uncertain to both.
• This leads to the following game that looks very
  much like the Cuban missile crisis!!

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Telling the Tragic Tale

• With the two additions the game looks as right
• p is the probability that Saddam is tough.
• q is the probability that the US will carry out
  its threat

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Telling the Tragic Tale
We solve the game by backwards induction.

• A tough Saddam will not quit since
• 8 lt 2 - 6q
• A soft Saddam will quit if
• 2 10q lt -4
• or q gt 0.6

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Telling the Tragic Tale
Now consider Georges options.

• George doesnt know if hes playing against a
  tough or soft Saddam.
• If he threatens he gets
• p(- 2 8q) (1- p)(1)
• If he doesnt threaten he gets
• p(-2) (1 p)(-2) -2
• So he threatens if
• p(- 2 8q) (1 - p)(1) gt -2
• or p lt 3/(3 8q)

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Telling the Tragic Tale.

• We know
• A soft Saddam quits if q gt 0.6
• Bush threatens if p lt 3/(3 8q)
• Saddam knows his type.
• Bush controls q.
• Bush may not know p.

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Telling the Tragic Tale.

• Suppose
• Bush doesnt know p.
• He experiments, first tries a
• q lt 0.6. If this doesnt work and doesnt
  trigger conflict he experiments again. Tries a
  slightly higher q. If this doesnt work, he tries
  again and so on.
• Either he reaches q 0.6 and a soft Saddam quits
  or he triggers a war.
• This is really no different from JFK and
  Khrushchevexcept the outcome!!