He explains why game theory tells us " that rational observers should conclude that failure to disclose relevant information implies that the information must be as damaging as it could possibly be. " Yet Donald Trump won't reveal his tax returns.
Frank presents a plausible (indeed convincing) explanation for our failure to act a agents in Nash's model would.
First he discusses the standard case in which the signal is a guarantee made by a producer to purchasers of the product.
Theory fails in this scenario for the same reason it seems to have failed for Trump’s tax returns: Seeing is believing. It’s one thing to deduce from an abstract theory that undisclosed information is as unfavorable as it could possibly be. But it’s quite another thing to witness unfavorable information firsthand. Because our powers of attention and imagination are limited, knowing there must be a bombshell in Trump’s tax returns is actually significantly less damaging than seeing the bombshell itself. (Think of your visceral reaction when you heard about Trump’s nearly $1 billion loss, compared with the vaguely negative impression you had of his tax situation beforehand.)
Frank is so stimulating that he stimulated me to defend the empirical relevance of the concept of Nash equilibrium. I don't believe the following argument at all, but I think it holds together. It is also possible that the apparent non Nash equilibrium actions are based on the theorists misunderstanding of the game people are actually playing.
Uninterestingly, it is always possible to make up a utility function to justify any behavior. So if Trump would find it horribly painful to publish his tax returns and doesn't care much about becoming president, then he wouldn't publish them even if they looked beautiful. If voters know this about Trump, then it makes sense to not infer anything from his secrecy. This argument is silly -- it is always possible to reconcile anything with Nash equilibrium by assuming people really really want to do whatever they did.
But I think there is a less silly defence in this case. Consider a low information voter who doesn't know whether Trump has released his tax returns (they may be few in number but they exist). This voter draws no inference from the unknown fact that Trump has kept his returns secret. However, if he were to release them and reporters were to discuss the bombshells at great length, it might get through to the resolutely news ignoring low information voter. Now if everyone who is paying any attention assumes that Trump's returns are as bad as they could be (without him actually being prosecuted). It becomes rational to keep them secret to avoid coming to the fugitive attention of the lowest information voters. This is a general issue. In the simple games used to discuss the issue, it is assumed that information transmission is perfectly efficient, so consumers know what sellers have made public. That's not the way I consume. I don't check if some product has a warrenty or guarantee before buying it. I don't read the limited warrenty after I buy it. I might check (maybe) if the product turns out to be defective. Since I don't know which products come with guarantees, it isn't easier to sell me a product with a guarantee. However, I have, in my life, taken advantage of warrenties (once or twice). If all consumers were like me, it would be best for producers of the highest quality products to make no guarantees.
Since I don't bother to check, I don't know what I have and haven't been told. In the models, it is assumed that I know this automatically and that it requires no effort at all to deduce the implications.
Again, I think Frank's explanation is correct and that this story is silly.