At some point early on in their economics education, every serious student of game theory will open a copy of Thomas Schelling’s 1960 classic The Strategy of Conflict. Economic theorists spent much of the next half century building the modelling tools to formalise and develop the ideas which were so brilliantly described by Schelling in his book. Just one famous example, on the importance of focal points for determining action in the presence of radical uncertainty was this:

You are to meet somebody in New York City. You have not been instructed where to meet; you have no prior understanding with the person on where to meet; and you cannot communicate with each other. You are simply told that you will need to guess where to meet.

Answer: a majority of (US based, at least) respondents were able to successfully coordinate at meeting at Grand Central Station at 12 noon.

As Putin’s Russia launches a full scale invasion into Ukraine, the return of war to European soil caused me to pick back up The Strategy of Conflict for perhaps the first time in about twenty years. Early on he covers the idea of Bargaining, Communication and Limited War. It seems particularly appropriate for the situation in which Europe now finds itself. Or it is at least to be hoped that we face only a limited war – and not the start of World War Three.

The essence of achieving limited war, says Schelling, is the difficult task of agreeing on the limits:

“Limited war requires limits; so do strategic maneuvers if they are to be stabilized short of war. But limits require agreement or at least some kind of mutual recognition and acquiescence. And agreement on limits is difficult to reach, not only because of the uncertainties and the acute divergence of interests but because negotiation is severely inhibited both during war and before it begins, and because communication becomes difficult between adversaries in time of war.”

And so it is now. Just yesterday, Biden called off plans for talks with Vladimir Putin.

So how does one achieve agreed limits on war in the absence of communication, and when interests diverge so strongly on opposing sides? Schelling’s original treatment of the issue is the phenomenon we all recognise today in the modern economic analysis of coordinated effects and joint dominance: tacit collusion:

The study of tacit bargaining – bargaining in which communication is incomplete or impossible – assumes importance, therefore, in connection with limited war, or, for that matter, with limited competition

The central problem with limited war, as with price coordination, is that rivals must, without the ability to communicate (or at least without the ability to trust each others’ communication) find a focal point for tacit agreement.

Schelling invites us to consider what happens when two commanders have opposing forces located at X and Y in the map below. Each wishes to avoid an armed clash and knows the other does too (for the sake or argument, let’s call them Joe and Vlad). Each must order their troops forward to take up a designated line – an

– if those lines overlap the troops will meet and fight;

– if those lines leave territory unoccupied between them, an unstable vacuum will also lead to conflict

The only stable situation in Schelling’s example is if the two commanders order their troops to take up identical but not overlapping positions.

Where would you order your troops?

From The Strategy of Conflict by Thomas Schelling

The answer, of course, is the river. “There is stability at the river – and perhaps nowhere else” says Schelling. Why? Because achieving tacit agreement on the limits of war is all about the rational expectations that one assumes to be forming in the mind of the opponent. In a power struggle, one cannot signal an unlimited willingness to compromise (since rivals will take maximum advantage), and so one automatically must look for alternatives that seem as salient as ‘lines in the sand’, which are qualitatively different such that they stand out as markers for “here but no further”.

Here’s how Schelling describes the river:

If some troops have retreated to the river in our map, they will expect to be expected to make a stand. This is the one spot to which they can retreat without necessarily being expected to retreat further, while, if they yield any further, there is no place left where they can be expected to make a determined stand. Similarly, the advancing party can expect to force the other to retreat to the river without having his advance interpreted as an insatiable demand for unlimited retreat.

So, argues Schelling, when we try to anticipate what the outcome of such conflicts might be we need to consider that “the outcome may not be so much conspicuously fair or conspicuously in balance with estimated bargaining powers as just plain conspicuous”.

And here we stand today in Europe. Wondering where our river will be. The game theory of limited war suggests that this will not be the start of World War 3 if a focal point can be found. A single line where both sides can simultaneously reasonably be expected to stop and think “here but no further”.

Is it the Donbas region? That seems unlikely given the scale of the offensive underway. Is it all of Ukraine? Surely that brings a bellicose Russia too close European Union borders. Yet if Kiev were to fall as some expect, this poses Schelling’s problem: once the capital is taken no other points other than Ukraine’s borders remain as natural stopping points.

This begs the question, could the answer be, once again, a river? The Dnieper river cleaves the country neatly in half north to south. And it would leave all the predominantly ethnic Russian parts of Ukraine under Putin’s control.

Image from unsplash.com

Another terrible thought is this: Putin may wish to take the Ukrainian capital in a show of force and as a signal of strategic commitment. Yet such a move would undoubtedly produce a bloody and full-throttled response from Ukrainian forces (supported, do doubt by Western materiel).

The Dnieper cleaves not just Ukraine but also its capital city – dividing Kiev into its Eastern and Western halves. And as the world knows from bitter experience, a city divided is a classic focal point for stalemate between world powers. It allows for partial retreat and partial victory on both sides – neither side holds nor gives up its claim to the centre of power. The people of the Ukraine would pay a terrible price, for no other reason than the need to establish a focal point for limited war.

Now of course, I am just an economist and no expert in military strategy, and I’m certainly no expert on Ukraine. But that was Schelling’s point: outcomes tend toward the obvious not the intricate in situations of limited war. The principles of tacit collusion apply:

In sum, the problem of limited warfare involves not a continuous range of possibilities from most favourable to least favourable, for either side; it is a lumpy, discrete world that is better able to recognise qualitative than quantitative differences, that is embarrassed by the multiplicity of choices, and that forces both sides to accept some dictation from the elements themselves. The writer suggests that the same is true of restrained competition in every field in which it occurs

Only a fool would try to predict the outcome of the current war with any certainty. But Schelling would encourage us to focus on the role of the game theory of tacit collusion in all this, and look for signs that a focal point is starting to emerge.