games people play. 11: brinkmanship – the tragic tale of george and saddam

Games People Play.Games People Play.

11: Brinkmanship – The Tragic Tale 11: Brinkmanship – The Tragic Tale of George and Saddamof George and Saddam


Brinkmanship GameBrinkmanship Game

You must choose a number between 1 and You must choose a number between 1 and 100.100.Your number is added to that of another Your number is added to that of another randomly chosen team.randomly chosen team.If the two numbers add to more than 100 If the two numbers add to more than 100 both teams are out of the game. both teams are out of the game. The game repeats 3 times in total.The game repeats 3 times in total.Each teams number is revealed to all the Each teams number is revealed to all the remaining teams after each round.remaining teams after each round.You cannot decrease the number you You cannot decrease the number you choose in any round.choose in any round.You may not raise your number by more You may not raise your number by more than 15 between any two rounds.than 15 between any two rounds.The winners are the last team “alive” with The winners are the last team “alive” with the highest number after three rounds.the highest number after three rounds.


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


BrinkmanshipBrinkmanship

One of the most important elements of brinkmanship is One of the most important elements of brinkmanship is

that the process must be somewhatthat the process must be somewhat out of controlout of control. . In the running across the road example, if the threatener In the running across the road example, if the threatener could listen or look to see if a vehicle were coming then could listen or look to see if a vehicle were coming then choose the probability of death by deciding when to run.choose the probability of death by deciding when to run.

But then the threat wouldnBut then the threat wouldn’’t work because all parties t work because all parties would know the threatener wouldnwould know the threatener wouldn’’t run if there were a t run if there were a vehicle coming. They would choose the probability zero. vehicle coming. They would choose the probability zero. Hence the probability of the threat actually being carried Hence the probability of the threat actually being carried out must be somewhat outside the threateners control.out must be somewhat outside the threateners control.


The Happy Tale of John and The Happy Tale of John and Nikita.Nikita.

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


The Happy Tale of John and The Happy Tale of John and Nikita.Nikita.

The Cuban Missile Crisis was an Example of The Cuban Missile Crisis was an Example of Success of the Brinkmanship Strategy.Success of the Brinkmanship Strategy.

JFK took the world to the brink of nuclear war JFK took the world to the brink of nuclear war and by doing so persuaded Khrushchev to and by doing so persuaded Khrushchev to remove missiles from Cubaremove missiles from Cuba..But it seems as if game theory cannot explain But it seems as if game theory cannot explain this. Why didnthis. Why didn’’t Khrushchev apply backwards t Khrushchev apply backwards induction, figure out the final outcome, and induction, figure out the final outcome, and decide not to start the whole process?decide not to start the whole process?More to come….obviously.More to come….obviously.


The Tragic Tale of George and The Tragic Tale of George and SaddamSaddam

JFK threatened Khrushchev and forced his compliance. JFK threatened Khrushchev and forced his compliance. Few shots were fired and there was no nuclear war.Few shots were fired and there was no nuclear war.He He ““gambledgambled”” and won. and won.GWB played a similar strategy against Saddam Hussein GWB played a similar strategy against Saddam Hussein ““gambledgambled”” and lost. He lost because the best outcome and lost. He lost because the best outcome was the compliance or removal of Saddam simply as a was the compliance or removal of Saddam simply as a response to Bushresponse to Bush’’s threat. The actual outcome was the s threat. The actual outcome was the removal of Saddam but only after a costly war.removal of Saddam but only after a costly war.Yet Bush and Kennedy played essentially the same Yet Bush and Kennedy played essentially the same strategy of brinkmanship.strategy of brinkmanship.Here we might ask why Saddam didnHere we might ask why Saddam didn’’t employ t employ backwards induction and quit before the war?backwards induction and quit before the war?


The Tragic Tale of George and The Tragic Tale of George and SaddamSaddam

We cannot say GWB in any sense played the game We cannot say GWB in any sense played the game better or worse than JFK.better or worse than JFK.

Brinkmanship necessarily involves taking risks. There is Brinkmanship necessarily involves taking risks. There is a chance of success and failure.a chance of success and failure.

Something went wrong in the Persian gulf that didnSomething went wrong in the Persian gulf that didn’’t in t in the Cuban missile crisis, but what was it?the Cuban missile crisis, but what was it?


A Simple Threat ModelA Simple Threat ModelSuppose GWB and SH each have two strategies Suppose GWB and SH each have two strategies

GWB - Threaten or Don’t.

SH – Quit or Stay.

A simple threat game then looks as follows A simple threat game then looks as follows

GWB

SH

Threa

ten

Don't

Quit

Stay

GWB, SH

1 , -4

-10 , -8

-2 , 2


A Simple Threat ModelA Simple Threat Model

The problem with the simple threat model is that The problem with the simple threat model is that backwards induction tells us GWB will always backwards induction tells us GWB will always threaten and SH will always quit…but this didnthreaten and SH will always quit…but this didn’’t t happen!! Saddam didnhappen!! Saddam didn’’t quit.t quit.Why?Why?Perhaps we have the payoffs wrong.Perhaps we have the payoffs wrong.Perhaps Saddam values defying the US and Perhaps Saddam values defying the US and simply prefers not to quit. simply prefers not to quit. This suggests the problem is that SaddamThis suggests the problem is that Saddam’’s s payoffs differ from those in the game above.payoffs differ from those in the game above.


Another Simple Threat Model.Another Simple Threat Model.

Here we see Saddam prefers to stay rather than quit.

But this explanation of events doesn’t work either. GWB should apply backwards induction and choose “Don’t”.

GWB

SH

Threa

ten

Don't

Quit

Stay

GWB , SH

1 , -8

-10 , -4

-2 , 2


Applying BrinkmanshipApplying Brinkmanship

Two elements are missing in our analysis of Two elements are missing in our analysis of the tale of George and Saddam.the tale of George and Saddam.

GWB didn’t know SH’s 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 Bush’s plans in the UN by France, Germany and Russia. But how much of a check there was on Bush’s actions was uncertain to both.

This leads to the following game that looks This leads to the following game that looks very much like the Cuban missile crisis!!very much like the Cuban missile crisis!!


Telling the Tragic TaleTelling 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

GWB

SH

Threaten

Don't

Quit

Stay

GWB , SH

1 , -8

- 2 -8q , 2-6q

- 2 , 2

SH

Threaten

Don't

Quit

Stay

1 , - 4

- 2 - 8q , , 2-10q

- 2 , 2

GWB

Nature

Tough Saddam Probability p

Soft Saddam Probability 1- p


Telling the Tragic TaleTelling the Tragic TaleWe solve the game by backwards induction.We solve the game by backwards induction.

A tough Saddam will not quit since

-8 < 2 - 6q

A soft Saddam will quit if

2 – 10q < -4

or q > 0.6

GWB

SH

Threaten

Don't

Quit

Stay

GWB , SH

1 , -8

- 2 -8q , 2-6q

- 2 , 2

SH

Threaten

Don't

Quit

Stay

1 , - 4

- 2 - 8q , , 2-10q

- 2 , 2

GWB

Nature




Telling the Tragic TaleTelling the Tragic TaleNow consider George’s options.

George doesn’t know if he’s playing against a tough or soft Saddam.

If he threatens he gets

p(- 2 – 8q) + (1- p)(1)

If he doesn’t threaten he gets

p(-2) + (1 – p)(-2) = -2

So he threatens if

p(- 2 – 8q) + (1 - p)(1) > -2

or p < 3/(3 + 8q)

GWB

SH

Threaten

Don't

Quit

Stay

GWB , SH

1 , -8

- 2 -8q , 2-6q

- 2 , 2

SH

Threaten

Don't

Quit

Stay

1 , - 4

- 2 - 8q , , 2-10q

- 2 , 2

GWB

Nature




Telling the Tragic Tale.Telling the Tragic Tale.

We know We know A soft Saddam quits if q > 0.6A soft Saddam quits if q > 0.6

Bush threatens if p < 3/(3 + 8q)Bush threatens if p < 3/(3 + 8q)

Saddam knows his type.Saddam knows his type.

Bush controls q.Bush controls q.

Bush may not know p.Bush may not know p.


Telling the Tragic Tale.Telling the Tragic Tale.Suppose Suppose

Bush doesnBush doesn’’t know p. t know p. He experiments, first tries a He experiments, first tries a

q < 0.6. If this doesnq < 0.6. If this doesn’’t work t work and doesnand doesn’’t trigger conflict t trigger conflict he experiments again. Tries he experiments again. Tries a slightly higher q. If this a slightly higher q. If this doesndoesn’’t work, he tries again t work, he tries again and so on.and so on.Either he reaches q = 0.6 Either he reaches q = 0.6 and a soft Saddam quits or and a soft Saddam quits or he triggers a war. he triggers a war. This is really no different This is really no different from JFK and Khrushchev…from JFK and Khrushchev…except the outcome!!except the outcome!!

games people play. 11: brinkmanship – the tragic tale of george and saddam

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