Shots in the dark. Game theory on prospects of war and Russia-Ukraine negotiations

Once the Russian state propaganda finished celebrating the capture of Bakhmut, which they portrayed as a remarkable triumph amidst an otherwise unsuccessful backdrop, it became evident that the Kremlin lacks a clear understanding of its future plan. Even Yevgeny Prigozhin, the owner of the Wagner PMC and also associated with a troll factory, openly acknowledged that, in the most optimistic scenario (a scenario he himself finds doubtful), Russia would only be able to retain the territories it has presently seized. Essentially, this implies that the Russian authorities have forsaken their third strategy of invading Ukraine and will now be compelled to propose a fourth alternative.

A history of failed strategies

The initial strategy, referred to as “capture Kyiv in three days,” relied on the involvement of GRU special forces and faltered primarily due to Ukraine's awareness of the plans devised by Russian secret services. The second strategy aimed at occupying the entire Ukrainian territory and imposing blockades on major cities. However, it quickly proved unsuccessful as Russian forces were ill-prepared for a full-scale war across such a vast area. In the autumn of 2022, Ukrainian forces launched a large-scale counteroffensive, pushing the conflict back to the southeastern region of the country. Following this, Russia underwent a significant shift in its approach to warfare and presented two new potential avenues for success.

The first approach was termed “partial mobilization.” According to Vladimir Putin, approximately 318,000 people were dispatched to serve in the armed forces. However, alternative assessments, relying on indirect indicators (although criticized for potential methodological flaws), suggest that the number of mobilized people surpasses 527,000. Regardless of the specific figure, even the lower estimates indicate that the influx of new soldiers is one and a half times larger than the entire Russian invasion force deployed in February 2022 (around 200,000 personnel). The Russian Armed Forces command reasonably anticipated conducting a significant offensive, such as the complete occupation of Donbass, through this mobilization effort.

The second approach was labeled as “strikes on energy infrastructure.” During the autumn of 2022, systematic attacks commenced, employing long-range precision-guided missiles and kamikaze drones, targeting Ukrainian energy facilities. The objective behind these strikes was evidently clear: to deprive the Ukrainian population of electricity and heating during the winter, instigate a humanitarian crisis, and ultimately weaken their resolve to resist. The expectations for success were significant, and within a span of a couple of months, the Kremlin managed to disable approximately a quarter of the power-generating capacity, leading Kyiv mayor Vitaly Klitschko to urge citizens to stock up on essential supplies such as food, water, and warm clothing.

The outcomes of the winter-spring campaign in Ukraine unequivocally point to the failure of these strategies. Mobilization efforts did not lead to a significant enhancement in the combat capabilities of the Russian forces. On the contrary, there was a decrease in the overall level of equipment and training. By examining the map depicting the changes in the front line from November 2022 to May 2023, the territorial progress made by Russian troops (highlighted in red) appears quite feeble and inconsequential.

Source

Likewise, the extensive missile attacks targeting the Ukrainian energy system ended in failure despite lasting for several months. During the period from October 2022 to May 2023, over 1,100 missiles (excluding kamikaze drones) were launched into the country, nearly depleting their supply. Out of these attacks, around 250 resulted in hits on energy facilities. However, the desired outcome of orchestrating sustained blackouts, even at the level of individual cities or regions, has not been achieved.

The Russian public is being prepared for peace talks

Russia is acutely aware of the current state of a positional stalemate in the conflict. In recent times, prominent propagandists and even some direct participants in the hostilities have been cautiously testing public opinion regarding the potential for peace talks and the conditions that could pave the way for such negotiations.

In February 2023, Alexander Khodakovsky, a prominent figure within the Donbass separatist movement and currently serving as the deputy head of the Rosgvardia Directorate in the “DNR,” expressed his views on negotiations with Ukraine via his Telegram channel. He asserted that not only are negotiations possible, but they are also “the only possible outcome of the confrontation.”

I hold the belief that achieving full territorial occupation of Ukraine and maintaining control over its disloyal population without resorting to perpetual violence is highly unlikely. If we were to attempt to swallow the entire chunk at once, we run the risk of encountering substantial difficulties. Therefore, given the present circumstances, it is crucial for us to establish clear advantages for ourselves, positioning us to engage in meaningful negotiations from a position of strength.

In March, Margarita Simonyan, the head of the propaganda channel RT, put forward a proposal during Vladimir Solovyov's TV talk show. Her suggestion involved a kind of “exchange” wherein Russian assets frozen in the West would be offered to Ukraine, possibly even labeled as “reparations.” However, the condition attached to this proposal was that the territories currently occupied by Russian armed forces, namely Kherson, Zaporizhzhia, Donetsk, and Luhansk regions, would remain part of Russia. Essentially, Simonyan's plan resembled a land purchase scenario, allowing people who desire to stay on the land to do so.

The prominent media figure of the current war stage, Yevgeny Prigozhin, known as the “owner” of the Wagner PMC, recently published an article containing a key thesis. Setting aside the patriotic rhetoric and customary criticisms of Ukraine and the United States, Prigozhin emphasizes the necessity of ending the war and declaring its conclusion under any conceivable pretext. In the article, Prigozhin presents one potential option: declaring the objectives of the special operation accomplished, specifically in terms of wearing down the AFU fighters, while simultaneously consolidating a foothold in (or “digging claws” into) the occupied territories of Ukraine.

Following the publication, Prigozhin faced the need to clarify his stance and maintain support for the continuation of the war. However, in a recent notable interview with pro-Kremlin political technologist Konstantin Dolgov, he essentially reiterated the notion of an ideal peace settlement, which he referred to as an “optimistic scenario.”

Europe and America will tire of the Ukrainian conflict. China will bring everyone to the negotiating table. We will agree that what we have already grabbed is ours, and what we have not grabbed is not ours.

Ukraine has firmly rejected the notion of engaging in negotiations and is currently preparing for a new counterattack. It is likely that Kyiv will succeed in reclaiming certain parts of Ukrainian territory. However, even the most optimistic observers do not anticipate the near-future return of Crimea and the entirety of Donbass. Consequently, following the counterattack, there will be a momentary lull, allowing both sides to regroup and gather strength. This respite will present a window of opportunity for potential negotiations.

War in Ukraine in terms of game theory

All participants engaged in discussions about peace talks and the resolution of the conflict between Russia and Ukraine, whether willingly or inadvertently, employ key concepts from game theory. For instance, analysts assert that Putin perceives the situation in Ukraine as a “zero-sum game,” wherein a victory for one side corresponds to a defeat for the other. Putin's thinking aligns with the geopolitical ideologies of the 19th century, wherein the annexation of new territories was deemed necessary to bolster a state's power. Consequently, Putin's objectives are framed within this paradigm, such as aspiring to establish a “land corridor to Crimea” or asserting the Sea of Azov as an “internal sea of the Russian Federation.” This approach renders mutually beneficial negotiations, or what game theory terms “win-win” scenarios, unattainable. Russia's gains are seen as directly proportional to Ukraine's losses in this perspective.

Today, the Kremlin's consensus position on demands boils down to four points:

• cessation of hostilities by the AFU and deliveries of Western arms;
• Ukraine's return to the neutral, non-aligned status enshrined in its 1990 declaration of state sovereignty;
• refusal to join NATO and the EU;
• recognition of new territorial realities resulting from the exercise of the right to self-determination by various populations (referring to the so-called referendums in the Zaporizhzhia, Kherson, Donetsk, and Luhansk regions).
  

These points indicate a notable decrease in the Russian president's ambitions, especially considering his initial demands for NATO to withdraw and revert to the borders of 1997. Initially, he had even prepared two puppet governments in anticipation of swiftly capturing Kyiv. The application of game theory enables us to retrospectively understand these transformations and formulate predictions by constructing optimal outcomes for all participants involved in this “game” (in this case, the war).

The Insider asked two renowned scholars, economist Konstantin Sonin of the University of Chicago (USA) and game-theoretician Branislav L. Slantchev of the University of California, San Diego (USA), to evaluate the prospects for a peace settlement in terms of game theory.

“The main problem for peace talks is the inability to bind Russia”

Konstantin Sonin, economist, professor at the University of Chicago (USA)

Game theory is not strictly a theory in itself but rather a set of tools and concepts that can be applied to various situations. It provides a framework for analyzing strategic decision-making and interactions among different actors. When we examine the current situation in Ukraine through the lens of game theory, we immediately notice the absence of a long-term equilibrium. Maintaining the status quo is not a viable solution, which implies the necessity of continuing attacks and seeking advantages. Consequently, international pressure is focused on urging Russia to withdraw its troops from Ukrainian territory, as this action would contribute to achieving a stable configuration and potential resolution.

One of the major challenges in achieving peace through partial concessions is the well-known commitment problem, which arises in game theory. The commitment problem refers to the difficulty of making binding commitments in strategic interactions. For Ukraine and its supporters worldwide, it is crucial not only to end the current war but also to prevent the outbreak of another conflict in the future. There is a widespread understanding that if Russian troops remain on Ukrainian territory, it would essentially be seen as preparations for future hostilities.

War can arise when one side lacks the ability to make credible commitments or when there is a significant lack of trust. This represents a fundamental challenge in establishing a truce or engaging in negotiations. In the context of Ukraine, President Zelensky's reluctance to negotiate with Putin stems from the concern that Putin has a track record of disregarding international treaties, breaking commitments, and undermining trust.

What approach can be taken to ensure that Russia refrains from further aggression and establish lasting peace? The solution, as perceived by Zelensky and the Western world at large, lies in reclaiming the occupied territories and forming a robust military force, potentially with the assistance of NATO. Given Russia's inability to provide trustworthy assurances, the only viable option seems to be implementing a clear and unambiguous solution that serves as a guarantee of peace.

Territorial conflicts are commonly perceived as zero-sum games, where one side's gain comes at the expense of the other. However, taking a broader perspective reveals that war itself has significant negative-sum consequences, inflicting losses on both sides. In reality, it would be mutually beneficial for both Ukraine and Russia to cease or prevent the war altogether. Ukraine's priority is to reclaim its territories, while Russia has the opportunity to choose a different path. From a national standpoint, it would be advantageous for Russia to end the conflict, withdraw its troops, and provide reparations for the damages caused by its aggression. This approach aligns with the broader interests of the country, even if it diverges from the personal interests of Putin as an individual leader. Recognizing the distinction between the interests of a nation and those of its leader is where our models and analysis can provide valuable insights.

“Russia would benefit from peace, but game theory suggests that as long as Putin is in power, peace is impossible”

Branislav L. Slantchev, specialist in game-theoretic analysis of war and peace negotiations, professor at the University of California, San Diego (USA)

The question of “why fight?” is deceptively simple. War is a very costly and risky way to resolve disputes, and since all wars eventually end, one can ask the question “Why couldn’t the opponents reach that outcome without fighting?” In principle, it can be shown that under very general assumptions, there always exist negotiated settlements that both actors would prefer to fighting. That is, settlements that give each of them terms that are at least as good as what they expect to gain from war. The question is what prevents them from finding these terms.

There are several answers, and all of them are relevant to the war in Ukraine. First, peace is not possible as long as each player expects to gain from fighting more than what the opponent is willing to concede. This is often called “mutual optimism” and gets interpreted that both sides believe in military victory. This is not the case, however, as the models clearly show that it is not necessary for both sides to believe in ultimate victory – “all” that is necessary is for them to believe that fighting (and then settling) would result in better terms than what the opponent is currently willing to offer. These beliefs can arise from a variety of factors such as estimates of own military superiority, resource advantage, morale, behavior of allies, and so on.

Before the war, all such estimates are hypotheticals – they are based on intelligence reports, observing military maneuvers, and analyses by experts. As such, they are subject to a lot of uncertainty and debate. In the current war, the initial Russian estimates about the Ukraine were very optimistic: they thought that Zelenskyy’s government would fall, that this would cause significant numbers of the Ukrainian military to switch sides (as had happened in 2014), that large numbers of Ukrainians would welcome them or at least acquiesce without a fight in the east and south, that the West would not be able to organize a response fast enough, and so on.

As we know, all of these estimates proved to be incorrect, for a variety of reasons mostly related to the corruption of Putin’s rule and changes in Ukrainian society since 2014. But – and this is important – there was no way of knowing any of this until fighting started. Experts can be wrong and people can lie to superiors but the battlefield does not. Within the first week or two of the war, the battlefield showed just how wrong these expectations were. It is also important to remember that the Russians were not uniquely prone to overestimating themselves and underestimating the Ukrainians – their expectations were widely shared in the West as well.

In the game-theoretic models, when an actor discovers from battlefield events that his original estimates were incorrect, he revises his beliefs about the trajectory of the war accordingly. In this case, the Russian side would have lowered its expecations of what it could obtain by further fighting. This should generally lead to a decrease in the demands that it will find acceptable. That is, since the fighting alternative now seems worse than before, the player should be willing to agree to peace on terms that are worse than the one he had originally demanded.

There is, however, an exception to that process, and it applies to players with a lot of unused resources that could be mobilized for further fighting. In that case, the actor will instead change his strategy – mobilizing more effort – in an attempt to restore the favorable war trajectory instead of compromising on his war aims. This is what the Russians did in April when they withdrew from Kyiv and focused on a slower conquest of the territories they wished to annex.

Now, every change in strategy often creates a host of new hypotheticals that can only be resolved on the battlefield. In this case, they were things like: will the West deliver enough weapons to Ukraine on time (initially, they had only supplied them with weapons useful in guerilla-style warfare because the expectation had been that this is the war they would have to wage), will the Ukrainian military be able to stop the Russian advances and perhaps recover lost territory? The Ukrainians outperformed all expectations, and according to the theoretic models, this should have two effects. Ukraine should raise its demands (this is when they started to talk openly and with increasing frequency about recovering Crimea), and Russia should lower its demands.

Russia opted to keep its war aims the same and increase its effort through mobilization. In addition to getting 300,000 new soldiers, the government began to transition the economy to wartime footing, and the Duma introduced many laws designed to stifle any remaining dissent in Russia. Mobilizing such numbers requires time, and so on the battlefield Russia switched to a delaying strategy of attrition to buy itself time to get ready for the new offensive. This did not prevent the Ukrainians from liberating Kherson, but the Russians did manage to evacuate all their troops and equipment from the right bank.

They then spent most of the winter attacking the energy infrastructure of Ukraine in an attempt to disrupt their preparations, lower their morale, and perhaps scare off the Europeans. It did not work, however (and there are models that help explain why!) and instead the West resolved to send main battle tanks and all the necessary supporting equipment.

As before, the change in strategy introduced new unknowns that would have to be resolved on the battlefield: can Russia equip all the mobilized men? Can it train them to be effective on the front? How will its economy do under increasing strain of sanctions, emigration, and worsening demographics? Given the Western decision to send serious equipment to Ukraine, the Russians would have about 6 months before it was integrated into the Ukrainian military and ready to use. They had to make a move before that happened.

In mid-January, the Russians launched their offensive and the battlefield revealed that their military is no longer capable of operating on a large scale and make any gains except local ones, and those at a very high cost. The offensive seems to be culminating now, and they have yet to capture Bakhmut, which they have been trying to take for over 280 days. They were repulsed at Vuhledar and Avdiivka with very heavy losses, and their advances in the north have been very limited as well.

The Russians, however, also spend a considerable amount of time constructing fortifications and they kept about 200,000 troops in reserve to defend them along the 800 km front. So now the key unknown – which is what the Ukrainian offensive will answer – is whether the Ukrainians are capable of breaching these fortified defenses and holding territory beyond them. They have not yet done so in the war (in Kharkiv, they broke through unprepared Russian lines, which panicked the rest and led to a collapse of the entire sector, and in Kherson their initial attempt to break through failed and only the threat of operational encirclement forced the Russians to evacuate), so it’s unclear. Moreover, we don’t know whether local breakthroughs are going to lead to collapse of sectors as happened last year.

Putin’s strategy now seems to be to outlast Western support for Ukraine – which would be necessary to force Kyiv to concessions – but for that the Russian military can demonstrate that the Ukrainians cannot dislodge them by force from Ukraine. This is why the coming Ukrainian offensive is important – the entire Russian strategy is predicated on holding onto the occupied territories and hoping that “something will happen” that would weaken Western resolve and force the Ukrainians to negotiate.

Given how often one hears about the “need to negotiate” in the Western media, I have to say that these calculations are not unreasonable. Russia has sympathizers in the West, it also have a lot of people fearful of escalation to nuclear war, and so there are people ready to sacrifice Ukraine.

Right now, there is no possibility for peace because the war expectations of the two sides are widely apart. The Ukrainians have yet to make their move and they appear optimistic about their chances, while the Russians appear convinced that their reserve troops would be enough to deny the Ukrainians their battlefield success. In the game theoretic model, fighting under such conditions must continue as it is the optimal strategy for both sides.

There are game theoretic models of war fighting that go down to soldiers/commanders level, and there are ones that remain at a very high level of abstraction where only “states” are considered. All have their uses. I like mid-level theories that isolate key decision-makers from the participants. In this case, I would look at models that involve a leader (Zelenskyy and Putin) and relevant domestic constituencies (this seems especially relevant in the Russian case), as well as 3rd parties (here I would consider “the West” as the relevant one).

One would then consider the mobilization potential of the various participants. For example, let’s take the economic side: Russia has vast resources but (a) seems unable to mobilize them efficiently; and (b) they are no match for the West – if the West chooses to mobilize appropriately, which is by no means certain as well.

Even though the Russian Central Bank has been very good at mitigating the effects of the sanctions and the Russians have proven inventive in finding alternative suppliers and import-substitutions, there are serious limits to what can be achieved under a full sanctions regime. The Russian economy will continue limping along but will be set back several decades. All of this will make the war harder to continue, but not impossible. A lot will depend on whether China would do more – right now it appears unwilling to do so – and whether the West would remain unified – right now it appears to have consolidated, but who knows in a year or two.

We have models of domestic politics that explain how dictators stay in power at the cost of inefficiency and how “coup-proofing” weakens the military and security apparatuses, but here one would have to know a whole lot more about the internal workings of the Kremlin to be able to make good use of such models.

The main takeaway would be that Putin appears to be fairly secure in power because the entire system is organized in a way that deters challenges, mostly because the various factions fear of who will come next, and nobody is certain that they can prevail over the others. For instance, my hunch is that Prigozhin is allowed to record these sensational videos because this is useful to Putin: anyone looking at Prigozhin cursing at the military and taking aim at oligarchs and rich Russians would think twice before trying to remove Putin because what happens if this “unleashes” Prigozhin and his Wagner troops?

For negotiations to become possible, the fighting should reach the stage where both sides have roughly similar estimates of what the war trajectory would look like. This would make it possible to have some sort of a mutually acceptable agreement because otherwise, as I explained above, no amount of diplomacy would help them reach one. In this case, the “game” is mixed-motive: it means that it has both elements of cooperation (the wish to avoid further fighting) and conflict (over the terms of the agreement). In these kinds of situations, the terms of the agreement are most likely to be determined by considerations about what would make the resulting peace sufficiently stable and attractive.

A lot of the territories that Putin wanted to annex are already out of reach, and likely to remain so, which will take them off the table at any negotiations. Whatever the Ukrainians liberate will also most likely be non-negotiable. The attempt at regime change failed, and of course there invasion consolidated a Ukrainian identity that will be distinctly anti-Russian for a long time. This means that the territorial goals can only be partially satisfied still, and the “denazification” (or, actually, “de-Ukrainization”) goal is going to be completely denied (except, of course, in any territory that the Russians occupy, where they will continue to conduct the policies whose results we have seen in Bucha and Izyum).

Since his invasion will certainly fail to deliver on most of Putin’s aims, Russia will remain a revisionist power whatever the resulting settlement is until there’s a change in government there, at the very least. Maybe beyond that, depending on what the new government looks like. From the perspective of peace, this means that Russia would have to be deterrede from attempting to revise the terms of the settlement by force over the foreseeable future.

Here we look at models with what’s called “endogenous peace terms”, which means the terms of the peace are such that neither side is willing to restart fighting instead of living with these terms. The models show that this can only happen through mutual deterrence: each side must expect that its gains from fighting will be outweighed by the gains of remaining at peace. In the models, this as achieved by maintaining sufficient military power, which is a drag on peacetime consumption but absolutely necessary to maintain the peace.

The immediate implications is that “demilitarization” of Ukraine is impossible – in fact, it is necessary that Ukraine retain one of the strongest militaries in Europe, trained and equipped on Western standards, and probably supported with service requirements much like Switzerland and Israel do. Ukraine would also have to have a vibrant defense industry capable of supporting such an army.

Even a modernized Ukrainian army is unlikely to be able to stand up on its own. This means that Ukraine would need guaranteed external support, which in practice means membership in a multilateral defense alliance with the United States, the United Kingdom, and Poland at a minimum. Most likely, this would mean NATO membership. Ukraine’s devastated economy is in desperate need of foreign investment and development aid, which means that Ukraine will become a member of the European Union. In other words, the requirements of deterrence immediately imply that Russia’s war aim – Ukraine's neutrality – will not be satisfied.

One can now see why Putin is unlikely to end the war while he’s in office: the terms that the Ukrainians can be reasonably expected to agree to, given the situation on the battlefield, essentially exclude nearly everything that Putin wanted to achieve with this war. Since he is not the one suffering the costs of fighting domestically (the Russian society does), our models tell us that such agency problems result in leaders making decisions that are to the distinct disadvantage of their own populations. In other words, the war will continue and it will impoverish Russia.

Whatever the Ukrainians have released, that, too, will likely not be negotiated.

Since an invasion would certainly fail to achieve most of Putin's goals, Russia would remain a revisionist power, whatever the final settlement - at least until the government changes. Or maybe even after that, depending on what the new government looks like. From the perspective of the world, this means that for the foreseeable future, Russia will have to be deterred from trying to revise the terms of the settlement by force.

Here we consider models with so-called “endogenous peace conditions”: that is, peace conditions are such that neither side is willing to resume fighting instead of living with those conditions. The models show that this can only happen through mutual deterrence: each side must expect that its benefits from fighting will not outweigh the benefits of keeping the peace. The models achieve this by maintaining sufficient military power, which detracts from peacetime consumption but is absolutely necessary for peacekeeping.

This means that the “demilitarization” of Ukraine that Putin so dreamt of will not happen now: Ukraine will now have to maintain in combat one of the strongest armies in Europe, trained and equipped according to Western standards and possibly supported by universal military service requirements, as Switzerland and Israel do. Ukraine must also have a dynamic defense industry capable of supporting such an army.

Russia will regain its military might in 5-10 years and will be able to challenge any world that her government does not like

Even a modernized Ukrainian army is unlikely to stand on its own without Western support. This means that Ukraine needs guaranteed external support, which in practice means membership in a multilateral defense alliance with at least the United States, Great Britain and Poland. And this most likely means membership in NATO. Ukraine's devastated economy desperately needs foreign investment and development assistance - which means that Ukraine must become a member of the European Union. In other words, demands for containment inevitably imply that another of Putin's dreams - Ukraine's neutrality - will not be realized.

Given all this, it is understandable why Putin is unlikely to end the war while he is in power: the conditions to which the Ukrainian side can be expected to agree, given the situation on the battlefield, rule out almost everything Putin wanted to achieve by this war. Because he is not alone in bearing the costs of war within the country (Russian society does), our models tell us that such problems lead to decisions by leaders that are clearly disadvantageous to their own populations. In other words, the war will continue, and it will impoverish Russia.