Obama’s Nuclear Posture Review has been revealed. The main changes:
(1) We promise not to use nuclear weapons on nations that are in conflict with the U.S. even if they use biological and chemical weapons against us;
(2) Nuclear response is on the table against countries that are nuclear, in violation of the N.P.T., or are trying to acquire nuclear weapons.
This is an attempt to use a carrot and stick strategy to incentivize countries not to pursue nuclear weapons. But is it any different from the old strategy of “ambiguity” where all options are left on the table and nothing is clarified? Elementary game theory suggests the answer is “No”.
First, the Nuclear Posture Review is “Cheap Talk”, the game theoretic interpretation of the name of our blog. We can always ignore the stated policy, go nuclear on nuclear states or non-nuclear on nuclear states – whatever is optimal at the time of decision. Plenty of people within the government and outside it are going to push the optimal policy so it’s going to be hard to resist it. Then, the words of the review are just that – words. Contracts we write for private exchange are enforced by the legal system. For example a carrot and stick contract between an employer and employee, rewarding the employee for high output and punishing him for low output, cannot be violated without legal consequences. But there is no world government to enforce the Nuclear Posture Review so it is Cheap Talk.
If our targets know our preferences, they can forecast our actions whatever we say or do not say, so-called backward induction. So, there is no difference between the ambiguous regime and the clear regime.
What if our targets do not know our preferences? Do they learn anything about our preferences by the posture we have adopted? Perhaps they learn we are “nice guys”? But even bad guys have an incentive to pretend they are nice guys before they get you. Hitler hid his ambitions behind the facade of friendliness while he advanced his agenda. So, whether you are a good guy or bad guy, you are going to send the same message, the message that minimizes the probability that your opponent is aggressive. This is a more sophisticated version of backward induction. So, your target is not going to believe your silver-tongued oratory.
We are left with the conclusion that a game theoretic analysis of the Nuclear Posture Review says it seems little different from the old policy of ambiguity.
Cheap Talk 
10 comments
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April 11, 2010 at 10:57 pm
afinetheorem
At some level, this is a commitment device. The President does not have exclusive authority over the use of weapons – he or she is bound by law. To the extent that the new NPR increases pushback from other areas of government (say, the military command if the reaction was meant to be immediate), then I think the game does change. In the context of a longer war, I would imagine that the current NPR is written into, for instance, base agreements with foreign countries, and that violation of that contract is indeed enforceable by removing the US base. In particular, I think very anti-nuclear nations (say, some in Europe) will be less hesitant to renew base leases if they knew that “mini-nuclear” bombs of the type nearly used in the Afghanistan war were off the table.
April 16, 2010 at 10:17 am
sandeep
Hi: Thanks for your comment and for comments on other posts.
The costs and benefits of using a mini nuclear bomb are not a function of the NPR. Even if we said we were not going to use them, we can always use them. Surely we can punished by other countries by taking away of bases etc of we use them. But that is also true now. The costs and benefits to these countries of removing bases is not a function of NPR either. In either words, the game is not a function of cheap talk and hence its equilibrium set is not a funtion of cheap talk.
Analysis above assumes complete information about parameters. Cheap talk can matter of there is private information the sender has. But my main claim is that in this game cheap talk does not credible convey private information as all equilibria are polling equilibria. I wrote a second post about this.
April 12, 2010 at 12:56 pm
Fred H Schlegel
Could you argue that this is less effective than ambiguity? Since all involved know that the new statements have little more meaning than the old statements in time of war, does this tact make other engagement less believable over time? (Truthful ambiguity over unenforceable specificity?)
April 13, 2010 at 5:28 am
Andrew Gelman
You write, “Hitler hid his ambitions behind the facade of friendliness while he advanced his agenda.”
Is this really true? My impression was that Hitler was pretty aggressive, in his rhetoric as well as his actions.
You could argue that Hitler was so evidently a bad guy, even at the time, that he had nothing to gain by talking nice. But, the point remains, that if “cheap talk” is really so valueless as you imply, there’d be no reason for anyone to do it at all. I think it might be more useful to model actors (such as “the U.S.” or “Germany”) as complex entities, and to consider that stated policies and goals might, at the very least, affect he balance of power in future intra-organizational struggles.
April 13, 2010 at 8:34 am
sandeep
Hi Andrew:
My point is not that cheap talk is useless in ALL games, only in some games. Indeed, in games of incomplete information where say a player knows his preferences but other players do not, cheap talk can be useful because it can convey the player’s private information.
But there is one key case where cheap talk is useless even in games of incomplete information: when a player i’s preferences over player j’s actions do not depend on player i’s preferences. In the nuclear story, this arises if the player i prefers that player j not acquire nuclear weapons, whether player i is itself rapacious, conciliatory or something in between. Then, player i will always send the message that minimizes the probability that player j arms and cheap talk cannot be informative.
Of course one can consider more complex games with many players but the two player case already has an insight that is worth explaining.
Also, I was thinking of Hitler signing a peace treaty with Neville Chamberlain but this was only to add color to my blog post. My logical argument does not depend on the Hitler example.
April 13, 2010 at 6:28 am
Stephen Haptonstahl
It is easy to dismiss cheap talk as meaningless, but it need not be. One danger is that once the listener decides that all cheap talk is meaningless, then it is: we have reached the “babbling equilibrium” always lurking in signaling games.
Folks who take a little (or a lot of) game theory and apply it too simplistically tend to reach unpleasant equilibria in their personal interactions — they tend to defect day-to-day, to put it nicely. Even John von Neumann advocated for nuclear first strike, but he didn’t anticipate the effects of uncertainty or bounded rationality on best responses.
Suppose the listener is not 100% sure that cheap talk is BS. (See Cromwell’s rule and the thoughtful comments of afinetheorem (above).) A change from 100% chance of nuclear retaliation to 99% chance might not seem like much change, but multiplied by the cost of getting nuked yields a large change in expected value. This may drastically change the best response of the listener.
Taking these things into accounts may yield a model too complex to solve easily. However, discarding the effects of uncertainty makes the model too simple to explain the behavior of folks who haven’t taken “enough” game theory.
April 16, 2010 at 10:07 am
sandeep
Hi Stephen: All cheap talk is not meaningless. In some games it helps, in some games it does not. I claim it is meaningless in this particular game. That is ALL equilibria are babbling equiibria. In other games chap talk may change the set of equilibria wrt game w/o talk.
If people think cheap talk is not BS I agree cheap talk matters. Of course it can go in any direction. E.g. If people think Obama is softer than Bush because of his nuclear review, then he may have to signal he is tough by taking a tough action. Then, the review was bad from the standpoint of conflict not good.
Without a plausible theory of the the listener who is not 100% sure cheap talk is BS, it is too easy to reach any conclusion analyst wants.
Thanks for your comment.
April 14, 2010 at 11:06 am
Polimath » Blog Archive » All Theorists are Normative (or run that risk)
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[…] do not know personally. So it was a nice surprise to see that Andrew Gelman left a comment on my earlier post and then wrote his own blog post. Andrew says: [I]f this “cheap talk” is useless, why […]
March 19, 2014 at 4:08 am
Fitria
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