Category Archives: War

Does Increasing the Costs of Conflict Decrease the Probability of War?

According to many popular theories of war, the answer is yes. In fact, this is the textbook relationship for standard stories about why states would do well to pursue increased trade ties, alliances, and nuclear weapons. (I am guilty here, too.)

It is easy to understand why this is the conventional wisdom. Consider the bargaining model of war. In the standard set-up, one side expects to receive p portion of the good in dispute, while the other receives 1-p. But because war is costly, both sides are willing to take less than their expected share to avoid conflict. This gives rise to the famous bargaining range:

Notice that when you increase the costs of war for both sides, the bargaining range grows bigger:

Thus, in theory, the reason that increasing the costs of conflict decreases the probability of war is because it makes the set of mutually preferable alternatives larger. In turn, it should be easier to identify one such settlement. Even if no one is being strategic, if you randomly throw a dart on the line, additional costs makes you more likely to hit the range.

Nevertheless, history often yields international crises that run counter to this logic like trade ties before World War I. Intuition based on some formalization is not the same as solving for equilibrium strategies and taking comparative statics. Further, while it is true that increasing the costs of conflict decrease the probability of war for most mechanisms, this is not a universal law.

Such is the topic of a new working paper by Iris Malone and myself. In it, we show that when one state is uncertain about its opponent’s resolve, increasing the costs of war can also increase the probability of war.

The intuition comes from the risk-return tradeoff. If I do not know what your bottom line is, I can take one of two approaches to negotiations.

First, I can make a small offer that only an unresolved type will accept. This works great for me when you are an unresolved type because I capture a large share of the stakes. But if also backfires against a resolved type—they fight, leading to inefficient costs of war.

Second, I can make a large offer that all types will accept. The benefit here is that I assuredly avoid paying the costs of war. The downside is that I am essentially leaving money on the table for the unresolved type.

Many factors determine which is the superior option—the relative likelihoods of each type, my risk propensity, and my costs of war, for example. But one under-appreciated determinant is the relative difference between the resolved type’s reservation value (the minimum it is willing to accept) and the unresolved type’s.

Consider the left side of the above figure. Here, the difference between the reservation values of the resolved and unresolved types is fairly small. Thus, if I make the risky offer that only the unresolved type is willing to accept (the underlined x), I’m only stealing slightly more if I made the safe offer that both types are willing to accept (the bar x). Gambling is not particularly attractive in this case, since I am risking my own costs of war to attempt to take a only a tiny additional amount of the pie.

Now consider the right side of the figure. Here, the difference in types is much greater. Thus, gambling looks comparatively more attractive this time around.

But note that increasing the military/opportunity costs of war has this precise effect of increasing the gap in the types’ reservation values. This is because unresolved types—by definition—view incremental increases to the military/opportunity costs of war as larger than the resolved type. As a result, increasing the costs of conflict can increase the probability of war.

What’s going on here? The core of the problem is that inflating costs simultaneously exacerbates the information problem that the proposer faces. This is because the proposer faces no uncertainty whatsoever when the types have identical reservation values. But increasing costs simultaneously increases the bandwidth of the proposer’s uncertainty. Thus, while increasing costs ought to have a pacifying effect, the countervailing increased uncertainty can sometimes predominate.

The good news for proponents of economic interdependence theory and mutually assured destruction is that this is only a short-term effect. In the long term, the probability of war eventually goes down. This is because sufficiently high costs of war makes each type willing to accept an offer of 0, at which point the proposer will offer an amount that both types assuredly accept.

The above figure illustrates this non-monotonic effect, with the x-axis representing the relative influence of the new costs of war as compared to the old. Note that this has important implications for both economic interdependence and nuclear weapons research. Just because two groups are trading with each other at record levels (say, on the eve of World War I) does not mean that the probability of war will go down. In fact, the parameters for which war occurs with positive probability may increase if the new costs are sufficiently low compared to the already existing costs.

Meanwhile, the figure also shows that nuclear weapons might not have a pacifying effect in the short-run. While the potential damage of 1000 nuclear weapons may push the effect into the guaranteed peace region on the right, the short-run effect of a handful of nuclear weapons might increase the circumstances under which war occurs. This is particularly concerning when thinking about a country like North Korea, which only has a handful of nuclear weapons currently.

As a further caveat, the increased costs only cause more war when the ratio between the receiver’s new costs and the proposer’s costs is sufficiently great compared to that same ratio of the old costs. This is because if the proposer faces massively increased costs compared to its baseline risk-return tradeoff, it is less likely to pursue the risky option even if there is a larger difference between the two types’ reservation values.

Fortunately, this caveat gives a nice comparative static to work with. In the paper, we investigate relations between India and China from 1949 up through the start of the 1962 Sino-Indian War. Interestingly, we show that military tensions boiled over just as trade technologies were increasing their costs for fighting; cooler heads prevailed once again in the 1980s and beyond as potential trade grew to unprecedented levels. Uncertainty over resolve played a big role here, with Indian leadership (falsely) believing that China would back down rather than risk disrupting their trade relationship. We further identify that the critical ratio discussed above held—that is, the lost trade—evenly impacted the two countries, while the status quo costs of war were much smaller for China due to their massive (10:1 in personnel alone!) military advantage.

Again, you can view the paper here. Please send me an email if you have some comments!

Abstract. International relations bargaining theory predicts that increasing the costs of war makes conflict less likely, but some crises emerge after the potential costs of conflict have increased. Why? We show that a non-monotonic relationship exists between the costs of conflict and the probability of war when there is uncertainty about resolve. Under these conditions, increasing the costs of an uninformed party’s opponent has a second-order effect of exacerbating informational asymmetries. We derive precise conditions under which fighting can occur more frequently and empirically showcase the model’s implications through a case study of Sino-Indian relations from 1949 to 2007. As the model predicts, we show that the 1962 Sino-Indian war occurred after a major trade agreement went into effect because uncertainty over Chinese resolve led India to issue aggressive screening offers over a border dispute and gamble on the risk of conflict.

The Power Shift Myth: Understanding Preventive War

Shifting power is often cited as an explanation for war. But the causal mechanism isn’t so straightforward.

While the concept of preventive war dates back to Thucydides’ and The History of the Peloponnesian War, the modern understanding is just barely in its third decade. In Rationalist Explanations for War, James Fearon conclusively shows that bargained settlements exist that leave both parties better off than had they fought. The puzzle of war is why wars occur despite this inefficiency.

One of Fearon’s answers is that power may shift over time. Although a rising state and a declining state may reach an efficient bargain in the future, the declining state may be better off securing a costly but advantageous outcome through war today. As much as the rising state might protest, it cannot credibly commit to maintaining the status quo distribution of benefits. Rather, it will eventually want to exploit its new found power by shifting the benefits in its favor.

This idea has taken off in international relations literature. It is now the textbook explanation of preventive war. (See Frieden, Lake, and Schultz, Kydd, or myself.) It also has obvious empirical implications—growing power implies more war—which many quantitative scholars have explored. (See Bell and Johnson, Schub, and Fuhrmann and Kreps for recent examples.) The literature is growing, and knowledge is accumulating. These are great things to see.

A Hidden Assumption
Unfortunately, the causal mechanism behind preventive war isn’t entirely clear, and the notion that power shifts alone cause war is a bit of a myth. One hidden assumption in the simple preventive war construction is that power growth is exogenous. That is, the rising state does not choose whether to grow or how. It simply does, as though power grows on trees.

Yet, in practice, most power shifts are endogenous. Raising an army, building new aircraft carriers, investing in missile defense, and designing nuclear weapons all require active decisions by the state. The basic model ignores this part of the process and instead jumps to the strategic tradeoffs once the state has decided how to shift power.

Thus, a natural question to ask is how endogenous power shifts impact the probability of war. Thomas Chadefaux addresses this in his aptly-titled Bargaining over Power article. Perhaps surprisingly, the war result reverses completely—in any instance that a preventive war would have been fought, bargaining over power leads to a peaceful outcome.

The intuition is straightforward once you work through the mathematical logic. A rising state really wants to avoid war today because fighting would take place on terms most disadvantageous to it. Thus, if it had to choose between undertaking a power shift that would induce preventive war and a smaller power shift that the declining state would acquiesce to, it would choose the latter. After all, a smaller (but realized) power shift is preferable to a costly war.

The New Puzzle
Of course, Chadefaux’s results only take us further down the rabbit hole. There is ample historical evidence to tell us that states fight wars to forestall shifts in power. What then actually causes preventive war?

The literature provides a variety of answers, which I will now attempt to synthesize. First, some power shifts may actually be exogenous. If demographic trends are at the root of a power shift, countries may be unable to effectively limit their future power. In civil conflicts, protesters may be unable resolve coordination problems in the near future, leading to dramatic shifts in power over a short period of time. This helps explain why autocratic regimes exert such great effort in controlling their citizens’ movements.

Fearon recognized that the commitment problem disappears when states can bargain over power. But when the object of value also confers military advantages, bargaining can break down when there are indivisibilities in the good. Chadefaux also showed that having distinct discount factors can lead to conflict even without those indivisibilities.

Implementing such an agreement may create other bargaining problems, too. Debs and Monteiro investigate a model with costly power shifts that declining states cannot effectively monitor. Declining states sometimes need to initiate wars so as to deter weapons construction they might not otherwise observe. My research looks to see whether offering concessions-for-weapons can resolve these issues. Fortunately, the answer is yes. However, in the book manuscript I am working on, such deals fail when there is uncertainty over the declining state’s willingness to intervene.

Undoubtedly, there are many more answers to why states fight preventive wars even when power shifts are endogenous. Sadly, though, this literature feels somewhat stifled given that new research often constructs models with exogenous power shifts without any justification for why states cannot negotiate over power.

Empirical Implications
I conclude by discussing some implications of endogenous power shifts. First, quantitative scholars should care greatly about bargaining over power. Although we have established connections between power shifts and war, the above theory indicates that the causal relationship is not obvious. For example, it might be that other bargaining problems cause to both power shifts and war. We need to think carefully about these higher-order issues and search for empirical evidence of them.

Policy-wise, this tells us a great deal about negotiations with Iran. If Tehran constructs a nuclear weapon, it must be doing so because it does not anticipate preventive war. Thus, one way the United States can hold Iran to its commitments under the Joint Comprehensive Plan of Action is to maintain a credible threat to fight a war should Tehran violate the agreement. Internalizing the threat, Iran would not build a weapon. This is perhaps the ideal for Washington—the American threat to invade does all the heavy lifting, allowing the United States to obtain its best policy outcome without actually paying the costs of war.


Understanding the Iran Deal: A Model of Nuclear Reversal

Most of the discussion surrounding the Joint Comprehensive Plan of Action (JCPOA, or the “Iran Deal”) has focused on mechanisms that monitor Iranian compliance. How can we be sure Iran is using this facility for scientific research? When can weapons inspectors show up? Who gets to take the soil samples? These kinds of questions seem to be the focus.

Fewer people have noted Iran’s nuclear divestment built into the deal. Yet Iran is doing a lot here. To wit, here are some of the features of the JCPOA:

  • At the Arak facility, the reactor under construction will be filled with concrete, and the redesigned reactor will not be suitable for weapons-grade plutonium. Excess heavy water supplies will be shipped out of the country. Existing centrifuges will be removed and stored under round-the-clock IAEA supervision at Natanz.
  • The Fordow Fuel Enrichment Plant will be converted to a nuclear, physics, and technology center. Many of its centrifuges will be removed and sent to Natanz under IAEA supervision. Existing cascades will be modified to produce stable isotopes instead of uranium hexafluoride. The associated pipework for the enrichment will also be sent Natanz.
  • All enriched uranium hexafluoride in excess of 300 kilograms will be downblended to 3.67% or sold on the international market.

Though such features are fairly common in arms agreements, they are nevertheless puzzling. None of this makes proliferation impossible, so the terms cannot be for that purpose. But they clearly make proliferating more expensive, which seems like a bad move for Iran if it truly wants to build a weapon. On the other hand, if Iran only wants to use the proliferation threat to coerce concessions out of the United States, this still seems like a bad move. After all, in bargaining, the deals you receive are commensurate with your outside options; make your outside options worse, and the amount of stuff you get goes down as well.

The JCPOA, perhaps the worst formatted treaty ever.

The JCPOA, perhaps the most poorly formatted treaty ever.

What gives? In a new working paper, I argue that undergoing such a reversal works to the benefit of potential proliferators. Indeed, potential proliferators can extract the entire surplus by divesting in this manner.

In short, the logic is as follows. Opponents (like the United States versus Iran) can deal with the proliferation problem in one of two ways. First, they can give “carrots” by striking a deal with the nuclearizing state. These types of deals provide enough benefits to potential proliferators that building weapons is no longer profitable. Consequently, and perhaps surprisingly, they are credible even in the absence of effective monitoring institutions.

Second, opponents can leverage the “stick” in the form of preventive war. The monitoring problem makes this difficult, though. Sometimes following through on the preventive war threat shuts down a real project. Sometimes preventive war just a bluff. Sometimes opponents end up fighting a target that was not even investing in proliferation. Sometimes the potential proliferator can successfully and secretly obtain a nuclear weapon. No matter what, though, this is a mess of inefficiency, both from the cost of war and the cost of proliferation.

Naturally, the opponent chooses the option that is cheaper for it. So if the cost of preventive war is sufficiently low, it goes in that direction. In contrast, if the price of concessions is relatively lower, carrots are preferable.

Note that one determinant of the opponent’s choice is the cost of proliferating. When building weapons is cheap, the concessions necessary to convince the potential proliferator not to build are very high. But if proliferation is very expensive, then making the deal looks very attractive to the opponent.

This is where nuclear reversals like those built into the JCPOA come into play. Think about the exact proliferation cost that flips the opponent’s preference from sticks to carrots. Below that line, the inefficiency weighs down everyone’s payoff. Right above that line, efficiency reigns supreme. But the opponent is right at indifference at this point. Thus, the entire surplus shifts to the potential proliferator!

The following payoff graph drives home this point. A is the potential proliferator; B is the opponent; k* is the exact value that flips the opponent from the stick strategy to the carrot strategy:

Making proliferation more difficult can work in your favor.

Making proliferation more difficult can work in your favor.

If you are below k*, the opponent opts for the preventive war threat, weighing down everyone’s payoff. But jump above k*, and suddenly the opponent wants to make a deal. Note that everyone’s payoff is greater under these circumstances because there is no deadweight loss built into the system.

Thus, imagine that you are a potential proliferator living in a world below k*. If you do nothing, your opponent is going to credibly threaten preventive war against you. However, if you increase the cost of proliferating—say, by agreeing to measures like those in the JCPOA—suddenly you make out like a bandit. As such, you obviously divest your program.

What does this say about Iran? Well, it indicates that a lot of the policy discussion is misplaced for a few of reasons:

  1. These sorts of agreements work even in the absence of effective monitoring institutions. So while monitoring might be nice, it is definitely not necessary to avoid a nuclear Iran. (The paper clarifies exactly why this works, which could be the subject of its own blog post.)
  2. Iranian refusal to agree to further restrictions is not proof positive of some secret plan to proliferate. Looking back at the graph, note that while some reversal works to Iran’s benefit, anything past k* decreases its payoff. As such, by standing firm, Iran may be playing a delicate balancing game to get exactly to k* and no further.
  3. These deals primarily benefit potential proliferators. This might come as a surprise. After all, potential proliferators do not have nuclear weapons at the start of the interaction, have to pay costs to acquire those weapons, and can have their efforts erased if the opponent decides to initiate a preventive war. Yet the potential proliferators can extract all of the surplus from a deal if they are careful.
  4. In light of (3), it is not surprising that a majority of Americans believe that Iran got the better end of the deal. But that’s not inherently because Washington bungled the negotiations. Rather, despite all the military power the United States has, these types of interactions inherently deal us a losing hand.

The paper works through the logic of the above argument and discusses the empirical implications in greater depth. Please take a look at it; I’d love to hear you comments.

My APSA 2014 Presentation: Policy Bargaining and International Conflict

If you are looking for something to do on Friday from 10:15 to noon, head over to the Marriott Jefferson room to see my presentation on Ideology Matters: Policy Bargaining and International Conflict. It is based on a joint project with Peter Bils. Here is the abstract:

Studies of bargaining and war generally focus on two sources of incomplete information: uncertainty about the probability of victory and uncertainty about the costs of fighting. We introduce a third: ideological preferences of a spatial policy. Under these conditions, standard results from the bargaining model of war break down: peace can be inefficient and it may be impossible to avoid war. We then extend the model to allow for cheap talk pre-play communications. Whereas incentives to misrepresent normally render cheap talk irrelevant, here communication can cause peace and ensure that agreements are efficient. Moreover, peace can become more likely when the proposer becomes more uncertain about the opposing state. Our results indicate one major purpose of diplomacy during a crisis is simply to communicate preferences and that such communications can be credible.

If you can’t make it, you can download the paper here, view the slides here, or watch the presentation below:

We Shouldn’t Generalize Based on World War I

As you probably already know, today is the 100th anniversary of the assassination of Archduke Franz Ferdinand, which would set off the July Crisis and then World War I. For the next few months, the media will undoubtedly bombard us with World War I history and attempt to teach us something based on it.

This is not a good idea. World War I was exceptional. To make generalizations based on it would be like making generalizations about basketball players based on LeBron James. LeBron is so many standard deviations away from the norm that anything you learn from him hardly carries over to basketball players in general. At best, it carries over to maybe one player per generation. The same is true about World War I. It was so many standard deviations away from the norm that anything you learn from it hardly carries over to wars in general. At best, it carries over to maybe one war per generation.

Anyway, the impetus for this post was a piece on Saturday’s edition of CBS’s This Morning, where a guest said something to the effect of “the lesson of World War I is that sometimes it is difficult to stop fighting once you’ve started.” (Apologies I don’t have the exact quote. They didn’t put the piece on their website, but I will update this post if they do.) I suppose this is true in the strictest sense–sometimes countries fight for a very long time. However, such long wars are rare events. Most armed conflicts between countries are very, very short.

To illustrate this, I did some basic analysis of militarized interstate disputes (MIDs)–armed conflicts that may or may not escalate to full scale war from 1816 to 2010. If we are interested in whether fighting really begets further fighting, this is the dataset that we are interested in analyzing since it represents all instances in which states started butting heads, not just the most salient ones.

So what do we find in the data? Well, the dataset includes a measure of length of conflicts. If fighting begets further fighting in general, we would expect to see very few instances of short conflicts and a much larger distribution of longer conflicts. Yet, looking at a histogram of conflicts by length, we find the exact opposite:


(I used the maximum length measure in the MIDs dataset to create this histogram. Because the length of a conflict can vary depending on who you ask, the MIDs dataset includes a minimum and maximum duration measure. By using the maximum, I have stacked the deck to make it appear that conflicts last longer.)

Each bin in the histogram represents 50 days. A majority of all MIDs fit into that very first bin. More than 90% fall into the first seven bins, or roughly a year in time. Conflicts as long as World War I are barely a blip in the radar. Thus, fighting does not appear to beget further fighting. If anything, it appears to do just the opposite.

One potential confound here is that these conflicts are ending because one side is being completely destroyed militarily. In turn, fighting begets further fighting but stops rather quickly because one side cannot fight any longer. But this is not true. Less than 5% of MIDs result in more than 1000 causualties and even fewer destroy enough resources to prohibit one side from continuing to fight.

So why doesn’t fighting beget further fighting? The simple answer is that war is a learning process. Countries begin fighting when they fail to reach a negotiated settlement, often because one side overestimates its ability to win a war or underestimates how willing to fight the opposing side is. War thus acts as a mechanism for information transmission–the more countries fight, the more they learn about each other, and the easier it is to reach a settlement and avoid further costs of conflict. As a result, we should expect war to beget less war, not more. And the histogram shows that this is true in practice.

Do not take this post to mean that World War I was unimportant. Although it was exceptional, it also represents a disproportionately large percentage of mankind’s casualties in war. It was brutal. It was devastating. It was ugly. But for all those reasons, it was not normal. Consequently, we should not be generalizing based on it.

Cheap Talk Causes Peace: Policy Bargaining and International Conflict

(Paper here.)

Here are two observations about international diplomacy:

First, crises are often the result of uncertainty about policy preferences. Currently, this is most apparent with the United States, Russia, and Ukraine. It remains unclear exactly how much influence Putin wants over Ukrainian politics. He might have expansionary aims or he may just want moderate control, aware that too much sway over Ukraine will cost Russia too much in subsidies in the long term. In the former case, the United States has reason to worry. In the latter case, the United States can relax.

Second, diplomatic conferences often discuss preferred policies. That is, the parties sit in a room and talk about what they want and what they don’t want. For scholars of crisis bargaining, this is weird. War, after all, is supposed to be the result of uncertainty about power or resolve or credible commitment. These types of discussions are seemingly cheap talk and are therefore supposed to have no effect on bargaining behavior.

In a new working paper, Peter Bils and I help explain these stylized facts. The first observation leads us to set aside the traditional sources of uncertainty–power and resolve–and instead focus on uncertainty over policy preferences on a real line, similar to the spatial model in American politics. The second observation suggests that we should study how cheap talk affects bargaining outcomes in such a world.

Our results are striking and run in contrast to the standard bargaining model of war. Rather than standardize policy preferences on a [0, 1] interval, we allow the winner of a war to endogenously decide what policy to implement afterward. This forces the parties to not only think about how likely they are to win a war and how much it will cost but also consider the quality of their post-conflict outcomes.

Without communication, we find that war may be inevitable–if your opponent’s preferred policy could range from moderate to very extreme, it is impossible to construct an offer to simultaneously appease all types. But if the range possibilities is smaller, peace can be inefficient. This is because the proposer may want to offer an amount that all types are willing to accept. Yet, in doing so, both the proposer and some types of the opponent would be both better off implementing a more moderate policy instead.

We then allow for cheap talk pre-play communication. Normally, cheap talk fails to cause meaningful change because weaker types have incentives to misrepresent; that is, they want to mimic stronger types to receive more generous demands. In some situations, this remains true in our setup. However, cheap talk can occasionally work when the uncertainty is about policy preferences. This is because moderate types sometimes do not want to bluff extremism since doing so would result in an intolerably extremist offer. As a result, where war was previously inevitable and peace was inefficient, peace always works and is efficient as well.

Empirically, this suggests that diplomacy is useful, which helps explain why states spend so much time and effort on it. And despite all of the incentives to lie, cheat, and bluff, those exchanges can sometimes be taken at face value.

Here’s the abstract from the paper:

Studies of bargaining and war generally focus on two sources of incomplete information: uncertainty about the probability of victory and uncertainty about the costs of fighting. We introduce a third: ideological preferences of a spatial policy. Under these conditions, standard results from the bargaining model of war break down: peace can be inefficient and it may be impossible to avoid war. We then extend the model to allow for cheap talk pre-play communications. Whereas incentives to misrepresent normally render cheap talk irrelevant, here communication can cause peace and ensure that agreements are efficient. Moreover, peace can become more likely when the proposer becomes more uncertain about the opposing state. Our results indicate one major purpose of diplomacy during a crisis is simply to communicate preferences and that such communications can be credible.

ISA 2014 Presentation: War Exhaustion and the Stability of Arms Treaties

If you are interested in nuclear weapons and negotiations with Iran, consider my panel at ISA. The panel title is “TD09: Solving Puzzles with Formal Models: A Panel in Honor of Dina Zinnes” and will be on Thursday at 4 pm. (The lineup is impressive: Dina Zinnes, Kelly Kadera, Mark Crescenzi, Songying Fang, Anne Sartori, and T. Clifton Morgan.) Here’s the abstract:

Why are some arms treaties broken while others remain stable over the long term? This chapter argues that the changing credibility of launching preventive war is an important determinant of arms treaty stability. If preventive war is never an option, states can reach settlements that both prefer to costly arms construction. However, if preventive war is incredible today but will be credible in the future, a commitment problem results: the state considering investment must build the arms or it will not receive concessions later on. Thus, arms treaties fail under these conditions. The chapter then applies the theoretical findings to the Soviet Union’s decision to build nuclear weapons in 1949 and Iran’s ongoing nuclear program today. In both instances, war exhaustion made preventive war incredible for the United States, but lingering concerns about future preventive war caused both states to pursue proliferation.

You can download the full paper here.