Should Trump Give North Korea A ‘Bloody Nose?’ What game theory has to say about targeted strikes and nuclear deterrence.

If someone punched you in the nose, what would you do? Does your answer change if he has a nuclear bomb? What if you do, too?

President Trump’s war of words with North Korea over its ever-improving nuclear program is a battle dictated by the tenets of game theory. Each side postures, responds and anticipates, trying to convince the other that it’s willing to fight and unwilling to back down. So far, it has been only a war of words.

But last week, The Wall Street Journal reported, citing unnamed officials, that “U.S. officials are quietly debating whether it’s possible to mount a limited military strike against North Korean sites without igniting an all-out war on the Korean Peninsula.” The limited strike, the article says, would target a North Korean facility as punishment for one of the country’s nuclear or missile tests. South Korea says that Trump told its president that the Journal’s report was “completely wrong,” and that there would be no military strike while the two Koreas were in ongoing diplomatic talks.

But despite Trump’s reported denial, the plan, which is nicknamed the “bloody nose” option, has prompted a fierce debate about its merits. And while it would change the state of play, it is also consistent with a “game” where convincing your opponent of your intentions is paramount.

The thing that keeps us all from blowing up during a nuclear standoff is something called deterrence: No country carries out an attack against any other because each is convinced that it will face devastating retaliation. It’s this delicate stasis that has forestalled nuclear war ever since there was more than one country with nuclear weapons.

To make deterrence work, a country will send signals to its enemy demonstrating its willingness to fight back — nuclear tests, military exercises, statements from the White House lawn … and, yes, tweets.

The bloody nose, in theory, would be another, more robust, signal of willingness. Talk — and tweets — are cheap, after all. The logic in the tactic’s favor goes something like this: The U.S. would be unlikely to take this drastic step if it were bluffing about its willingness to launch a full attack on North Korea, perhaps even with a nuclear weapon. North Korea would realize that, and perhaps the U.S. could win some concessions. Or so the theory goes.

The argument against the bloody nose is just the same — it could prove very costly. Deterrence can quickly become escalation. North Korea has many options for retaliation, and it could inflict massive casualties on the Korean Peninsula or in Japan even with its conventional weapons. It is also now reported to have the ability to launch a long-distance strike on the U.S. mainland. If North Korea responded to its bloody nose, the U.S. would likely respond, and North Korea would likely respond to that, and so on.

“It’s pretty symmetrical,” Robert Powell, a Berkeley political scientist who studies game theory and war, told me. “The North Koreans would be asking fundamentally the same questions” about strikes and retaliation that the U.S. is asking, so we could expect them to do fundamentally the same things.

The calculation for the U.S. is how much risk it’s willing to take on to make its case that North Korea should stop its nuclear and missile testing.

“It’s like an auction. You know you have some limit and you hope the other guy backs down before you reach your limit,” Powell said. The currency of the bids, in this case, is how much each country is willing to risk all-out war.

“Ultimately, you’d like to convince the North Koreans that the U.S. would engage in a large war to prevent North Korea from acquiring the capability to launch nuclear attacks against the U.S.,” Powell said.

(Hypothetically, there may be another low-cost way to ratchet up the pressure a little bit: Leak a bloody-nose battle plan to The Wall Street Journal.)

David Kang, the director of the University of Southern California’s Korean Studies Institute, was blunter in his assessment.

“The ‘bloody nose’ option is the dumbest thing I’ve ever heard from D.C.,” Kang told me. “North Korea is incredibly consistent: If we hit them, they will hit us back. There is no possible way that they will just accept it.”

As an example, Kang pointed to a pair of events from eight years ago. In November 2009, South Korea shot up a North Korean ship in disputed waters off the peninsula and one North Korean sailor was killed. Sure enough, four months later, a South Korean warship was sunk.

Specifically, Kang thought it likely that North Korea would respond to a bloody nose by attacking bases in Japan. Thousands of American troops and civilians live in Japan and South Korea.

“They are not crazy. They are not unpredictable,” Kang said of North Korea. “They are the most predictable country in the world.”

We’ve covered the bloodless nuclear standoff with North Korea before. In September, I wrote more extensively about the game theory that governs these confrontations. This month, our editor-in-chief Nate Silver and I discussed Trump’s infamous button tweet on our latest FiveThirtyEight Politics podcast.