War and Dilemmas

Upon listening to the narrative of the classic prisoner's dilemma (refer to the provided link), it is natural for one's mind to seek a simple solution. In my imagination, before their capture, I envisioned the prisoners making a pact to stand by each other and not betray one another. This seems plausible, doesn't it? The problem would be resolved. Similarly, the characters in the bar scene needed to reach an agreement to work together (see my last blog post for details).

Our mind tends to arrive quickly at solutions, but it takes significant effort and a moment of realization to understand that, in some cases, a simple solution does not exist. The players in these scenarios are doomed not to cooperate. Believing in a quick fix disregards the situation's fundamental reality. Much like escaping gravity's pull may be possible temporarily, gravity will always assert itself; in the prisoner's dilemma, defection is almost certain. 

To grasp the dynamic, let’s get as far away as possible from the trivial nature of the bar scene and the story of the two prisoners. Let’s up the stakes to a conflict where nearly 20 million people died - WW I.

The Onset of War 

The world in the lead-up to WW I was relatively peaceful and prosperous. And then, suddenly: 

"The lamps are going out all over Europe, we shall not see them lit again in our life-time," ~ British Foreign Secretary Sir Edward Grey

The statement is frighteningly accurate when one considers the ripple effects of World War I. Without the first World War, it is highly probable that World War II would not have occurred, and there would have been no Cold War. Some historians even suggest that the Great Depression may not have happened. While it is difficult to say for certain, it's important to note that the impact of the war did not end on November 11th, 1918. The aftermath of the war continued to have significant and long-lasting effects on the world.

Despite the immense scale of the conflict, it was instigated by countries that were attempting to protect themselves. Neither side sought to start a war, yet they found themselves embroiled in a conflict so devastating it was referred to as "The Great War." This seemingly paradoxical outcome begs the question of how this could happen.

In the renowned book "The Guns of August" by Barbara Tuchman, the author narrates the events leading up to World War I, skillfully demonstrating how both sides of the conflict perceived themselves as acting defensively. From the book:

"The system of alliances and counter alliances, of secret understandings and public promises, of military plans and mobilizations, of strategic calculations and diplomatic exchanges, which the powers had built up through the nineteenth century as the means of preserving peace, had become the most dangerous and unstable structure of all." ~ Tuchman

It is challenging to convey all the complex dynamics at play, but in essence, the conflict began with Europe dividing into two groups of strategic alliances to protect against one another. At the time, the formation of these alliances was seen as a great achievement that would promote peace. The thinking was that if both sides were powerful and well-prepared for war, neither would ever consider invading, thus leading to peaceful coexistence. However, in order to maintain this balance of power, both sides began amassing weapons and military resources, creating an arms race to ensure they were always on equal footing.

As both sides built up arms, they began to suspect the other might invade; in defense, they continued to build up arms…. And so forth.

As history tells it, Germany initiated the invasion in World War I. While it is crucial to understand who made the first move, it is also important to recognize that the underlying cause of the conflict was the perception both sides had of one another. As a result, the build-up of military power and the swift response by France and Russia was inevitable.

Both nations had prepared for war out of fear of being invaded and were operating from a defensive stance. This is supported by historical accounts indicating that Germany genuinely believed they would be attacked. The fuse was lit with the assassination of Archduke Franz Ferdinand.

The Formal Game

Below is a tool referred to as a decision matrix that illustrates the dynamic. The matrix below might seem confusing, but it is quite simple. Both sides have the same choices; the parties here are the Allies and the Central Powers (CP for short). The payoff to the Allies/CP for an action given the counterparty's action is the first/second number in each box.

Thus, if the Allies declare war and the CPs declare war, then the Allies get -1, and the CP gets -1. To better illustrate that these can be different. If the Allies choose war, but CP chooses peace, the Allies get 2, and CP gets -2. For completeness, if the Allies choose peace and CP war, it is -2 for the Allies and 2 for CP. If both choose peace, we end up in the 2nd row, and 2nd column, and both get zero.

The numbers here don’t have any concrete meaning. They represent something relative to each other (0 is better than -1, -1 is better than -2, etc.). If you like, you could think of them as total wealth a side gets given a particular set of actions. Perhaps think of them as billions of dollars in GDP, but it isn’t that important. 

The idea, which is the important part,  is simple enough. Both sides are best if they invade while the other is not expecting it; they get 2. The idea is they get all the other country's resources – it is an easy win. If both sides are at peace, they are the same as before. 

If both sides choose to defect and go to war, they both end up with a negative outcome, represented by -1. This is better than the option of being caught off guard and attacked while undefended but worse than the alternative of maintaining peaceful relations with each other. This reflects the reality of the war; it dragged on and resulted in immense devastation; while the Allies ultimately emerged victorious, both sides lost greatly in the end.

Now, the most important part, why were both declaring war unavoidable? The best way to answer is a counterfactual - suppose they didn’t. Suppose one side decided not to build up arms and be at the whim of the other. Well, the other would find it too beneficial and invade. Both sides thinking the same way made it unavoidable. 

To think in terms of the matrix, put yourself in the war and war column and row and realize neither country would be better off moving. If they went with peace, they would go from -1 to -2. Thus, we arrive at Nash’s true insight and the dilemma - the situation is destined to result in doom, and once the gloomy outcome is realized, neither side has the incentive to deviate.

Think of a western showdown. Neither side wants to be stuck holding their gun at the other, but it is only wise to lower their weapon once the counterparty does first. The equilibrium is for both to keep their weapons drawn indefinitely…

So what's the solution? Well, join me for part 3.