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The study of modern history is currently undergoing a revolution. That is largely because historians are beginning to apply the ideas in network theory to the complex interactions that have forged our past.

There was a time when historians focused largely on events as the be all and end all of history. But in recent years, there has been a growing understanding that a complex network of links, alliances, trade agreements and so on play a hugely important role in creating an environment in which conflict (or peace) can spread.

An interesting open question in this regard is whether certain kinds of networks exist that are stable against the outbreak of war. Today, we get an answer thanks to the work of Matthew Jackson and Stephen Nei at Stanford University in California. These guys combine network theory and game theory to study the stability of different kinds of networks based on real-world data.

In particular, Jackson and Nai study the theoretical properties of networks consisting of countries that have military links and compared them to the properties of networks in which countries have both military and trade links.

Finally, they apply real data to their model. They combine international trade data with the well-known “Correlates of War” database to see how closely their predictions match those of real networks.

Jackson and Nei begin by considering a simple network of a handful of countries that can form military coalitions of various strengths. At the same time, each alliance must serve a purpose by helping to protect the countries involved so that the deletion of any alliance would make a country vulnerable. In this network, a country is vulnerable to attack if its coalition is weaker than its opponents’ coalition and the cost of a war is less than the benefit.

An interesting question is whether such a network can ever be stable against war. In other words, can the network exist in a way that no country is vulnerable to a successful attack by others and that no country can change alliances in a way that makes such an attack viable.

Jackson and Nei use game theory to calculate mathematically that this kind of stability is impossible. “It turns out that there are no war-stable networks,” they say (except for the trivial case of an empty network with no links).

The reason is that the pressure to ensure that all alliances are purposeful makes the network unstable almost by design. “The pressure to economize on alliances conflicts with stability against the formation of new alliances, which leads to instability and would suggest chaotic dynamics,” they say.  “This instability provides insights into the constantly shifting structures and recurring wars that occurred throughout the nineteenth and first half of the twentieth centuries.”

Between 1820 and 1959, there were 10 times as many wars per year on average between each possible pair of countries than between 1960 and 2000 (see diagram above). So what has changed since the 1950s?

Jackson and Nei argue that it is the formation of trade links between countries that has created the stability that has prevented wars. Between 1816 and 1950, a country had on average 2.525 alliances but this has grown by a factor of four since then.

They go on to add this to their model. They point out that there has been a rapid increase in global trade since World War II, not least because of the advent of container shipping in the 1960s.

Next, they consider a network in which a link can exist because of a military alliance or because of economic considerations. This change dramatically alters the stability of the resulting network for two reasons.

First, trade provides a reason to maintain an alliance. Second, these economic considerations reduce the incentive to attack another country since trade will be disrupted. “This reduces the potential set of conflicts and, together with the denser networks, allows for a rich family of stable networks that can exhibit structures similar to networks we see currently,” say Jackson and Nei, a result they are able to show mathematically and which matches the real-world data after the 1960s.

Some historians might point out that there has been another factor at work since World War II: the development of nuclear weapons. Jackson and Nei say that nuclear weapons certainly change the landscape by increasing military strength and reducing the incentive to attack given the likely ensuing damage.

Indeed, their model suggests that the worldwide adoption of nuclear weapons could stabilise the global network in the absence of trade. However, their analysis also shows that the only solution for a stable network is the empty network in which there are no alliances. In this model, nuclear weapons do not play the role that many historians have claimed and cannot by themselves produce the network of links that exist today.

“To explain the much denser and more stable networks in the modern age along with the paucity of war in a world where nuclear weapons are limited to a small percentage of countries, our model points to the enormous growth in trade as a big part of the answer,” say Jackson and co.

That is a fascinating insight into the way conflicts can be prevented. The complex link between trade and conflict is increasingly the focus of study. But little has been done to protect the game theoretical stability of these networks.  “To our knowledge, there are no previous models of conflict that game-theoretically model networks of alliances between multiple agents/countries based on costs and benefits of wars,” they say.

That makes this an interesting and important step forward and the basis on which a number of new ideas can be tested. For example, Jackson and Nei could include much more detailed information about the nature of trade links. And they could also include the role that geography plays in conflict, which is hard to model. “Geography constrains both the opportunities and benefits from trade and war, and so it has ambiguous effects on stability,” they say.

Another important consideration is the relative rates of economic and military growth. Do countries that outgrow their competitors economically protect themselves against future conflict?

The best models also have predictive power. There is an interesting analogy with forest fires, which can occur on a wide range of scales, some many orders of magnitude larger than others. The size of these fires is almost entirely dependent on the network of links between trees in the forest. If these links are sparse, the fire dies out. But if they are dense, the fire can spread easily.

A crucially important point is that the eventual size of the fire has little, if anything, to do with the spark that started it. So an analysis that concentrates on this spark will inevitably ignore a great deal about the nature of the fire.

The same kind of thinking applies to a wide range of social phenomena, such as epidemics, fashions, wars and so on. And it allows interesting predictions, for example, that the size distribution of epidemics, fashions and wars should all follow the same pattern, which turns out to be observed. It also suggests that the initiating event is a poor predictor of the eventual size of an epidemic, fashion or war.

So an interesting task for future modellers will be to use these kinds of simulations to predict where future areas of conflict might occur and how they can be protected against.

That is a big ask, not least because the changing nature of international alliances, whether economic or military, is hard both to measure in real-time and predict of any decent timescale. Nevertheless, these are all worthy goals.

Ref: : Networks of Military Alliances, Wars, and International Trade

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