It’s always nice when you get a comment from someone you recognize but 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 it’s done at all! Or, conversely, why it wasn’t done earlier. Baliga’s analysis seems to me to rely on there being some “suckers” somewhere who don’t realize what’s going on.

Perhaps, for example, the leaders of Iran, Russia, etc., aren’t fooled by the cheap talk.–after all, they run countries and have incentives to understand the relevant signaling–but maybe it could sway American voters, who don’t have the time and inclination to gain a deep understanding of power politics. But . . . if it could fool the voters, it could change U.S. policy, and in that sense the stated policy does mean something. Beyond this, there are default effects and status quo effects and costs to violating or altering a stated policy. So I don’t think such public statements are necessarily meaningless, especially considering the many players involved in policymaking in any country.

On the other hand, I know next to nothing about international relations, so I could well be missing something important. I don’t see Baliga’s conclusions as following from basic game theory but maybe there’s something about this particular setting that changes things.

I was a bit terse in my original post and the concept of “cheap talk” is confusing so let me have another stab at an explanation.

Cheap talk is a costless message sent before a game is played.  Since it is costless, you might think it never has an impact.   That turns out not to be true. But whether and how cheap talk has an impact depends on the game that’s played after the talk.

The simplest and most famous scenario is where the game just involves a decision made by one player, the receiver (this is the famous Crawford-Sobel model).  In the background, there is some uncertainty and the receiver would love to fine-tune his decision to the underlying state.  If he does not know the state, the receiver makes a decision which works out on average and this is the equilibrium of the game without cheap talk.  Now add  a player, the sender, who knows the state and whose preferences coincide exactly with the sender’s.  Let the sender send a message before the receiver makes his decision.  The sender has perfect incentives to tell the truth, so the receiver learns the true state in equilibrium and cheap talk works.  That is, the equilibrium set of the game without cheap talk is different than the game with cheap talk.  Hence, cheap talk can be effective even if it is costless.  It does not require the existence of suckers.  And cheap talk is useful as it helps the two players to some to the best decision in each state.  (Actually, Jeff has already written about this game.)

But in the nuclear proliferation scenario I claim cheap talk is not useful.   I copy my initial response to Andrew:

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.

As  player i sends the same message whatever his preferences, his message contains no information.  Hence, the equilibrium set does not change compared to a nuclear proliferation game with no talk preceding it.  Whatever player j’s optimal plan was in the game without cheap talk, it remains optimal with cheap talk.  Some message is sent in any case – even saying nothing is a message.  There will always be some message, like it or not, once you allow cheap talk before a game.  The question is whether it is effective and I claim it is not in my visualization of the nuclear proliferation game.

My analysis is a rational choice analysis, as is analysis in basic game theory.  It assumes in particular that Iran is rational.  This means they can do backward induction and think through Obama’s strategic incentives to send messages.  Then, they can deduce that he always has the incentive to minimize their probability of acquiring weapons whether he intends to be belligerent, conciliatory or not.  So, there is no information content in the message as the same message in sent in all cases.

Gelman makes the point that if voters can be fooled, cheap talk may be effective.  Also, if Iran is fooled, cheap talk is also effective.  This latter possibility is the hypothesis that makes sense of the new nuclear policy in the simplest way – if Iran accepts Obama’s message at face value, it might stop pursuing nuclear weapons.  If Obama believes that Iran is naive, he does want to send the message.  But, as Andrew suggests, the idea that Iran would be caught out is implausible.  If even if Obama believes there is small chance Iran/North Korea is fooled, he may send it anyway – after all I claim the policy has no impact anyway if Iran is rational but if it makes things better with a small probability, why not?

Andrew’s idea that voters might be fooled is plausible and his post built around this idea.  (Somewhat confusingly, he suggests I am assuming there are suckers in the model but I think his idea requires them while mine is a rational choice analysis.) But anyway, till we have a good theory of how to fool voters, it is hard to judge how the change in nuclear policy affects nuclear proliferation.  If voters think Obama’s policy is a softening of the previous policy and will embolden Iran, as the Cheneys will say, voters may think Obama is weak.  Then, Obama may have to signal he is tough by acting tough, not just talking tough.  So fooling voters is bad for Obama in the end and he is a sucker too in this scenario.  Or we can go the other way and say voters will increase support for Obama as he is a smart foreign policy guy and will reduce nuclear proliferation.  Then, the Obama strategy makes sense.  We can send the analysis anyway we want by adding players who can be fooled into the story.

But there is an insight to the basic game theory analysis – why might communication not work?  It would be good to understand that before moving on to add naive voters, status quo effects and the like.