Will Russian President Vladimir Putin use a first-strike tactical nuclear weapon in Ukraine if he cannot succeed there by conventional means? What are the odds?

So, it turns out that “the odds” are likely irrelevant in this type of conjecture. The Pentagon instead is more likely at this moment exploring many variations of a mathematical model with the ironic name of game theory. Except that when you bring nukes into the picture, you get a “game” that has no winners.

I grew up in the 1950s and remember well the nuclear war school drills and public service announcements, reaching a zenith with the 1962 Cuban Missile Crisis as the Soviet Union’s Nikita Khrushchev attempted to position ballistic missiles in Cuba, ninety miles south of Florida. The breakup of the Soviet Union 30 years later frayed a lot of nerves with a then-unstable Ukraine sitting on one-third of the fast-dissolving USSR’s intercontinental missiles with nuclear warheads.

And it is “déjà vu all over again” another 30 years later, again with the Un-SSR’d Russia. Bloomberg reports:

“Before invading, Putin staged nuclear weapons drills around Russia’s border with Ukraine. In case anyone missed the point, his speech justifying the invasion reminded listeners that his country remained ‘one of the most powerful nuclear powers.’…Worse, this rant went hand in hand with a sinister warning: ‘Whoever tries to hinder us, and even more so, to create threats to our country,’ he declared, would suffer ‘consequences that you have never encountered in your history.’ Next came his announcement that Russia’s nuclear forces had been put on a ‘high alert.'”

In March of 2018, I wrote about North Korea’s belligerent nuclear threats in this blog, and talked about a vitally relevant, mathematical model long used by the Pentagon to strategize war. I used as illustration the 1983 film WarGames, starring a young Matthew Broderick. In the film, Broderick, as a young computer hacker messing around in Pentagon computer systems, gets greeted by an ominous 1983-era digitized voice: “Shall we play a game?” (click below to listen.)

The “game” Broderick comes across in the film appears to be a computer simulation called Global Thermonuclear War, but things get out of hand, and the computer seems bent on starting a real nuclear war. Spoiler alert! War with the USSR is averted at the last minute when the computer “realizes” (with Broderick’s help) that that the only viable solution to the “game” Global Thermonuclear War is to “refuse to play the game” in the first place.

From the 1983 film WarGames.

Apparently Russian President Vladimir Putin neither watched that movie (which admittedly does get a bit cheesy in spots) nor read my blog posts. And so, here we are.

From Games to Economics

The birth of modern probability theory is often credited to Italian mathematician Gerolamo Cardano (1501–1576) who was seeking an edge in winning games of chance. Jump ahead to the world war years of the 1940s and Hungarian-American mathematician John von Neumann (1903–1957) tackled games for which basic probability math was inadequate for optimizing a solution.

In some games, as well as with macroeconomic models of the economy that von Neumann then tackled, a dilemma arises because the outcome depends primarily on what the other guy does. And not just in probabilistic chances of winning but by radically divergent outcomes. Some of the potential outcomes, even if the probability is low, are disastrous, and yet out of your control. Definable probability goes out the window and basic uncertainty rules the show. And while pundits on television may throw out their predicted probabilities on uncertain events, that percentage number is more opinion confidence (or bluster) than statistics.

Therefore, there is no “correct” decision in most game theory situations before the fact. The span of results often has these “catastrophe functions” where the outcome varies radically depending on how the other guy responds to your actions. However, von Neumann found ways to model some of these thorny economic problems as pseudo-games, and thus economic game theory was born.

The card game blackjack is an example of a game that is both stochastic (containing provable probabilities with a 52-card deck) and finite (the probabilities converge toward a zero-card deck). Both the player and the dealer are constrained in their choices by specific rules. Because of those constraints, you can map out the long-term theoretical results of strategies, especially using computers. The house has a statistical edge in the long run, but there are blackjack strategies that may pay off in the short run for the most knowledgeable (or lucky) players.

Chess, on the other hand, adds the unpredictability of the other side, which slowed the objective of a chess-playing computer until IBM’s Deep Blue supercomputer defeated Russian Grandmaster Garry Kasparov in 1997, and even then only barely, thanks to one draw. Deep Blue relies more on a “brute force” approach to the solution rather than a statistical one, depending on a library of 700,000 grandmaster games. The major accomplishment of Deep Blue was its algorithms to traverse an almost infinite number of position and play options in “real chess time,” which does employ probability (and enables loss).

From Biology to War

The models of game theory were extended to biology by John Maynard-Smith in the 1970s, and he won a Nobel Prize for that work. He used a thought exercise, called the “Hawk-Dove Game,” to mathematically model competition for a shared resource, not just among humans, but in all of evolutionary animal life. One universal survival strategy throughout time he calls conciliation (“share”) while the alternative is conflict (“fight”).

There two options of behavior for each party yielding a 4×4 matrix of outcomes. In human terms, imagine a hunter-gatherer extended family encountering another clan inside “their” hunting territory. I have called this “the first ethical dilemma” because it has no single “good answer.” While one of these outcomes has the smallest “downside,” that outcome depends on both parties understanding the “game” that they are in, and on both parties choosing to step down from dominance to accept “half a loaf.”

The British philosopher/mathematician Bertrand Russell applied this game, more commonly known as “Chicken” in its most basic form, to describe the 1950s-60s USSR versus USA nuclear “brinkmanship.” He famously said, “Both [the USSR and the US] are to blame for playing such an incredibly dangerous game.” [1] In that same Cold War era, the classic film 1955 James Dean film Rebel Without a Cause features teenagers playing a literal game of “Chicken” with their cars, and with a tragic outcome.

But it is not as simple as Russell contended. If one person decides to start playing the “Global Thermonuclear War” game, it is arguably impossible to not join the game yourself. Each side blames the other for starting the game. And here we are.

Signaling a solution

Central to game theory is the concept of signaling, where the best way to break through to a solution is often to “signal” a message to the other party in order avert mutual destruction. To our hunter-gatherer forebears, human language itself became the key. If you could communicate a message to the other party that, for instance, you spoke the same language, or you had common ancestors, or even worshiped the same God, the odds of shifting the outcome to a “share-share” scenario were greatly improved.

The story we were told about the 1962 Cuban Missile Crisis confrontation was that Nikita Khrushchev backed down after President Kennedy threatened to invade Cuba to remove Russian nuclear weapons there. Later evidence confirms, however, that a complex web of under-the-radar “signaling” operations were going on, seeking a way for Khrushchev to save face to his own government. We only learned later that the U.S. quietly committed (and “quietly” is the operative word) to remove Jupiter missiles from Turkey in return for the Soviets removing their missiles from Cuba. That was likely the signal that enabled the stand-down.

Unfortunately, many American “hawks” still believe that our resolve alone ended the nuclear crisis and averted Armageddon. They are wrong, and that kind of prejudice can skew war gaming (and warring itself).

Our religions and social structures have continued to evolve into very complex, many-layered “signaling systems” that normally keep us from killing each other. But they are still very dependent on the actions of the “other,” who is often just as frightened of us as we are of him (and it has almost always been “him”). The “other” is playing the same game as we are playing, facing the same dilemma that we are. Sometimes the signaling works, and sometimes it doesn’t.

Minimizing the risk of escalation

Much of game theory application to war games is in the evaluation of potential escalation scenarios, as these inevitably steer the game toward “worst case outcomes.” And probability is less important here than is a clear mapping of possible “worst case” scenarios.

For instance in Ukraine, NATO leaders have clearly “gamed out,” correctly so far, that increasing the provision of sophisticated defensive weapons, such as shoulder-mounted Javelin anti-tank missiles, would not escalate the conflict there. However, the reluctance to directly supply MiG fighter jets by either Poland or the U.S. suggests that the calculation in both capitals has determined that adding these jets to the mix could be a “bridge too far” toward escalation. Establishing a NATO-enforced “No-fly Zone” has also been nixed thus far, apparently by most NATO nations, as far too escalatory.

However, scenario-building and war-gaming are surely continuing throughout NATO. And, we can only hope, Russia as well. Potential de-escalating strategies are floated as well. Should Ukraine offer to stay out of NATO? Should President Zelenskyy cede the Ukrainian territories on the Russian border to Putin’s control? The point here is that whatever “odds” the television pundits put on these things, Mr. Putin is not rolling dice. He is seriously playing the game to its fullest.

Theologian James M. Robinson has written, “The human dilemma is, in large part, that we are each other’s fate.” One man’s hubris has us at war in Europe. Another man’s hubris has destroyed faith in America’s elections & public health system. Our human fate depends on getting both of these men out of the game.

Here is the four-minute spoiler ending to WarGames (1983).

Related posts:

• North Korea and Game Theory
• The first ethical dilemma

Notes:

1. Poundstone, William. “Prisoner’s Dilemma.” Poundstone on the Game of Chicken. Who Will Defect First?