Game theorists: NATO needs to convince Russia everything is still on the table
I don’t normally write about current events, but, as a mathematician, I felt compelled to point out the flaws in how NATO is dealing with…
I don’t normally write about current events, but, as a mathematician, I felt compelled to point out the flaws in how NATO is dealing with the Ukrainian conflict right now. In particular, the President has taken the most powerful bargaining chip off the table in dealing with Russia: direct conflict between Russian and NATO forces.
It isn’t surprising why Biden has chosen this path. He is a product of the Cold War era where Mutually Assured Destruction (MAD) was the order of the day. But even then, the concept didn’t make mathematical sense.
The idea of MAD comes from a game theoretic concept which Zagare and Quackenbush refer to as classical deterrence theory. In this theory, war (between superpowers) is considered to be the least desirable outcome by all rational actors.
It turns out, however, that, if one makes this assumption, classical deterrence theory is unstable, you cannot maintain the status quo. Thus, by assuming a classical model of deterrence, NATO leaders are almost guaranteeing that in the end, Russia will win not only this conflict but the next and the one after that.
Counterintuitively, the best way to maintain the status quo (i.e., peace) is to be willing to fight.
To illustrate what I’m talking about let’s take an asymmetric game in which you have two state actors, A and B, which represent, e.g., the superpowers making choices about how to proceed. (Much of this analysis comes from Chapter 4 of Game Theory: Modeling Interstate Conflict by Quackenbush and Zagare.)
State A here begins the game with two choices: status quo (cooperate with the given world order) or defect (seek to change the world order). In the case of status quo, everything stays as it is and the game ends. Should it choose defect, State B must then choose how to respond. It has two choices: concede or deny. Should State B choose concede, then State A wins.
One solves for the correct choices in this game by working backwards from the expected outcome to the choices that each State should make. In the case of State B, the desired outcome is status quo, while for State A, the outcome is A wins.
Classical deterrence theory assumes that all actors are rational, i.e., they will make choices that maximize their interests. Each state assumes that the other one is rational as well. If conflict is the least desirable outcome for both States A and B, then A and B know that the other will never make a choice that results in conflict. Hence, in trying to determine what choice it should make, A will work out that State B will avoid conflict at all costs and choose as its initial move defect (this is the move Putin has made against NATO by invading Ukraine). Based on a rational assessment of the moves, this will always lead to B concedes and A wins.
What this means is that classical deterrence theory is unstable in this kind of asymmetric contest. State B will avoid getting into direct conflict with State A. Since A knows that, it will choose to upset the status quo every time. There is never a time when a stable equilibrium is reached.
Some researchers attempt to resolve this problem by having one State feign irrationality. If State A believes State B is irrational, then it may choose to maintain the status quo. This certainly works to an extent, but it is far more likely to be disbelieved.
We need not abandon rationality or the appearance of rationality, here, however.
Perfect deterrence theory is an alternative to classical deterrence theory that does lead to stable equilibrium. It maintains perfect rationality but gets rid of the assumption that States will necessarily avoid conflict at all costs.
This comes down to two core features of deterrence theory: threat credibility and threat capability. If a threat is credible, it means that a rational actor would carry out an action that they threaten, i.e., such an action would maximize their own reward. If a threat is capable, that means that threat would exact sufficient cost to deter the threatened. If both of these conditions exist, then they must be taken into account in the game calculus, working from outcomes up to decisions.
Consider applying this to our simple game above. If State A believes that State B offers a credible and capable threat, then it cannot assume that State B will choose to avoid conflict. In this case, State A may choose to maintain the status quo and the equilibrium is rescued.
State A is particularly likely to choose to avoid conflict itself if State B’s threat capability is overwhelming. In other words, if State B is likely to win any toe-to-toe conflict that ensues, State A will choose the status quo.
Let’s now use the conflict between NATO and Serbia in the late ‘90’s Kosovo conflict as an example. In this case, bloody war and ethnic cleansing on the part of the the Serbian dictator Slobodan Milošević caused NATO to get involved in the conflict between Serbia and the KLA. At first NATO decided it could make a show of being threatening by staging a massive display of airpower just outside the border. This threat was not seen as credible, in part because NATO was not united on how to proceed with the USA believing it could act unilaterally while other members wanted the blessing of the UN Security Council.
Eventually, NATO escalated to a limited bombing campaign. This not only killed innocent people but failed to deter the aggressor. Clearly, the dictator believed NATO would not go any further, and he had good reason.
Unfortunately, like President Biden, Bill Clinton in an address stated that the US and NATO did “not intend to put our troops in Kosovo to fight a war”. Thus, while NATO was willing to get involved, it was not willing to escalate and hence gave the Serb dictator the rationale he needed to continue.
Escalation is a critical piece of the theory that makes the simple two move game into a multi-move game. In an asymmetric game of escalation, the game above is more complex. Each side has not two but three choices. It can concede, respond in kind (continue the conflict as is), or escalate. In the Kosovo war, Clinton made sure that the Serbs knew that NATO would not escalate even if the Serbs did, and that is exactly what happened.
In a contest of escalation, State A (the challenger in the escalation game) must believe that State B (the defender) is willing to escalate or it will continue its campaign, rationally believing that they will eventually win by avoiding major conflict with State B.
Bluntly stating a refusal to escalate was Clinton’s (and President Biden’s) mistake.
Clinton corrected his mistake two months after his original statement however, saying that NATO would not “take any options off the table” and built up ground forces in neighboring Macedonia and Albania. This implicit threat to escalate from bombing to sending in ground troops may have been what led to Serbia pulling its forces out in June, 1999. NATO peacekeepers entered then to stop the killing. Rationally, Milošević knew he could not win a ground war with NATO. NATO’s threat was both credible and clearly capable.
The relevance to today’s conflict in Ukraine is that if Russia thinks NATO (State B above) is unwilling to escalate conflict from, say, financial pressure and supplies to bombing to ground troops and make that threat credible to Russia (State A above), Russia will win.
Perfect deterrence theory assumes rational actors, so what of reports that Putin is “unhinged”? These reports are likely based on a failure to understand game theory, a failure to realize that Putin is actually acting rationally. A more sinister possibility is that the reports are originating from Russia itself in a disinformation campaign to convince NATO that he is willing to start a nuclear war over this conflict because he is “crazy”. If he convinces us that he is willing to escalate as far as possible, then he will win. We must convince him that we are not afraid to intervene to all degrees necessary to force him to back down and further that we do not consider his nuclear threat to be credible. (Biden has shown that he does not find credible the Putin nuclear threat since he refused to escalate US nuclear readiness in kind.)
Threat capability may be another open question. Can NATO go toe to toe with Russia? Given reports about how poorly Russia is carrying out its campaign, its low morale and poor coordination, it seems likely that in a unified non-nuclear escalation NATO would win but only at enormous cost. At issue however is the cost to the Russians should it occur and whether that would be tolerable to them versus a negotiated settlement of some kind.
While the overall goal needs to be one of providing off-ramps and face saving opportunities for Putin to either pull out or at least cease fire, it isn’t clear that insisting that NATO has no intention of escalating beyond a certain point has any strategic benefit. In a game of chicken, indicating you will turn aside if the other driver gets to a certain point only encourages them to reach that point as quickly as possible. The only way to de-escalate is to give your opponent a rational reason to back down and make them want to cut their losses. If the enemy doesn’t know how far you will go, that is an enormous advantage. Setting red lines simply encourages Putin to continue his bullying behavior and escalate things further on his own terms and to the point he is comfortable with.
All of this suggests that President Biden, like Clinton, needs to roll back his statements about being unwilling to go into direct conflict with Russia and put everything back on the table, and NATO needs to increase its build up of forces in neighboring nations as it did in the Kosovo conflict.
While talks of no-fly zones now are premature and of dubious value, nothing should be off limits as the situation evolves.
There are risks of course. If Putin feels his own regime is at stake, he could be willing to engage in all out conflict. He must feel that his best option is to achieve some semblance of his objectives at the negotiating table and that the alternative is failure. NATO’s job is to ensure the inevitability of that failure is apparent and that further escalation on Russia’s part is undesirable. Russia’s nuclear capability is of concern, but launching nuclear strikes directly against NATO nations is not a likely rational action on their part (does not lead to them reaching their goals). Indeed, any attack on NATO members would demand that all members respond with force. Launching them against Ukraine is of higher concern. If we become convinced that nuclear war is an inevitable consequence of escalation, however, we will be playing into Putin’s hands.
Quackenbush, Stephen L., and Frank C. Zagare. “Game theory: Modeling interstate conflict.” Making sense of IR theory (2006): 98–114.