Upon hearing about the latest terror alert, which unlike most previous alerts actually names specific targets threatened by Al Qaeda, I reacted skeptically. “If I were a terrorist,” I thought, “and if I knew that counter-terrorist organizations were actively trying to thwart my plans, what would I do? Ah, yes: I would make it look like I’m targeting some location I don’t actually plan to attack, so the authorities would be distracted while I put my real plot into action.”
Then I had second thoughts. They have lots of smart people working at the intelligence agencies. Well, maybe not so smart, given recent failures; but surely smart enough to have thought of the point above. So they should be thinking, “If there is clear evidence that terrorists are casing targets A, B, and C, that’s really evidence that they are trying to distract us, and they plan to attack some other targets D, E, and F instead.”
But wait a minute. Those terrorists are pretty wily. They could presumably duplicate both lines of reasoning above, and then think to themselves, “If we make it look like we’re planning to attack sites A, B, and C, the intelligence agencies will think we’re trying to distract them, so they’ll focus their attention on sites like D, E, and F. Then we can attack A, B, and C after all!” And then the counter-terrorists would think, “The terrorists, in making it look they’re taking A, B, and C, are trying to mislead us into thinking they’re actually targeting D, E, and F, but in fact they are indeed targeting A, B, and C…”
This is a classic game of double-think. We could spiral through endless layers of “I know that you know that I know that you know…” without ever reaching a decisive conclusion. The structure of this game is identical to that of Matching Pennies, the Holmes-Moriarty game, and the Sneetches game. The only equilibrium of this sort of game is a mixed-strategy equilibrium, wherein both players (in this case, terrorists and counter-terrorists) randomize over their possible actions. I conclude that the current terror alert, which represents the counter-terrorists’ random response to the terrorists’ random evidence-creation, provides us with no information whatsoever.