Is War a Zero-Sum Event?


In game theory and economic theory, a zerosum game is a mathematical representation of a situation in which a participant’s gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s).

War is brutal and it is terrible, but it is not binary in nature. One does not “win” just because one “loses”. There can be many victors or none at all, but there is never an equal amount exchanged, one part given, one part received. The loss or gain from a military engagement is never, ever equal on both sides. If we think of warfare in the terms of a chess match then yes, this is true. Warfare and geopolitics, however, are extremely more complicated than moves on a boar. Bare with me for a short time and try to think of war pragmatically, devoid of the emotional burden which cannot be measured through exercises in game theory or by any other means.


To prove my point that war is never a zero-sum exchange, consider war as simple conflict. In its most brutal and basic form it would be just combat between two individuals, both presumably equal. Consider, now the death of a single person, the loser. That person’s death, a commonplace event in a warzone, socially and economically speaking, represents the end of any possible gains from their labor or any possible cultural contributions to a nation that he may ever produce. These are assets to a culture that are potentially invaluable. Considering the alternative, a nation may not have the means to support an individual, no matter how brilliant, to achieve their potential. What good is a world class software engineer in a nation with no power? In this case their loss represents one less mouth to feed, one less vaccination, one less series of resources expensed. This liability is finite though; there is only so much a person can take up. Therefore, in theory at least, a person lost is almost surely a net loss. Furthermore, it is almost surely more of a loss to the nation than is the bullet sacrificed by the enemy, and the gain that the victor has achieved is, in this case negligible. In this case, he walked away with only what he started with, his life. Ergo, in this example, warfare, when taken to the very base form, one person who lives, one who doesn’t, is a negative-sum event.

That said, there is also the possibility of positive-sum. When one nation overtakes another nation, it incorporates its surviving members, assets, resources and entire remaining capacity into its own. If this were the end of the story, we have a zero sum. Of course, this is not the end of the story. After the bullets have flown and mourning period has passed, the long run consequences and economies of scale take effect, new connections are formed, technologies are exchanged and the “empire” is capable of producing more value for both itself and its new citizens than either were capable of alone. This is why war can not be measured like exchanges on a chessboard, with a simple exchanges of resources. It can, however,be compared to RISK if we consider what happens when you capture enough territories. At some point, a person who has captured enough territories on the map gets a bonus, say if you capture all of North America. If you capture the right combination of territories and can hold them, you receive extra resources that would not exist at all if two or more players controlled the same spaces. In the real world, we might consider Russia’s recent intervention in Ukraine to be such an event. Considering the gain to Russia’s infrastructure that control of access the Baltic Sea and Ukrainian energy resources will have on the “new” Russia. It will experience much more economic and political power growth overall than the Ukraine has lost. This isn’t to say the Ukrainian loss is marginal; it is crushing to them, but the growth in Russia will potentially dwarf the losses experienced by the Ukrainians in the long run. So too, perhaps, will Russia’s next possible incursions as well. There is also much to say about how well this placed Russia politically in regards to force projection, international standing, discrediting NATO and the UN as well as the improved ability it now has to dictate policy throughout much of the old Soviet Union’s sphere of influence. To put it frankly, Russia’s total gain from Ukraine is immeasurably more than the simple value of the land and resources now lost to the powers of Kiev.

Then there is also the question of whether war, the very practice of organized violence has brought us all to the point of social prosperity we enjoy today. Stanford classics professor Ian Morris tries to argue this in his book, War! What Is It Good For? Conflict and the Progress of Civilization from Primates to Robots. A historian and an archaeologist, Morris believes that we left caveman status when stopped hunting large game as our only source for survival, and started turning our spears toward each other in a more organized fashion.

…”by fighting wars, people have created larger, more organized societies that have reduced the risk that their members will die violently.”

If we consider this as even a possibility, one might ask if the whole of civilized Earth we know today, is in fact the extremely long run result of wars effect to bring about new efficiencies and social structures. It’s only a theory, but one worth investigating, both as a society and as individuals.

This argument is, of course, ignoring the loss of human life, but not because of the tragedy and drama that comes with it. Pain heals and people move on. It is a reality of the human condition. I say this callously, but consider this fact that I am speaking as former United States Marine and Iraq War veteran. I have lost friends in war and good people I knew with much more to offer the world than the potential they were given. I’ve also seen first hand the results of a war on the people there. Before you decide to rebuke me for my insensitivity, know that I have thought much more about warfare than you likely ever will. From my experience, you should consider that a blessing. Know also, the way one deals with war isn’t to dismiss it as barbaric. Any civilized person knows war is a terrible event so you shouldn’t pat yourself on the back too hard for being aware of this. It is to attempt to understanding why wars happen practically, and their long term consequences practically and not allow your objective rationally to be muddled through emotionally charged, one-liner humanist tropes, impossible to deny, but themselves of little value. If you want to solve warfare, you need to truly attempt to understand it a little bit better. That said, pain heals and people move on.

From a world standpoint there is a great deal of importance to temporary nature of human suffering caused by human death. You don’t think it is temporary? Name all four of your grandparents right now. First names. To those who can, name all eight of your great-grandparents parents. Still a good person? Name four great-great-grandparents. That’s only 1/8th of them. If humans did not have a means to move on and forget tragedy, these people would haunt you even though you never knew them. The truth, they didn’t even haunt your grandparents enough that they made sure you remembered them. At some point we all die. Those who need us will inevitably find others to lean on. Those who need us for love will find others to love. Those who need us for material wealth will find other sources for income. Those who need us for guidance and motivation will find other teachers and perhaps, if we are lucky, be furthered by our memory. No one can replace your brother, your friend, you mother, your wife, or your dog, but the qualities these people, yourself, provide to the world can be found elsewhere. In a macro scale, this is even easier. If a business person dies, his customers will send flowers to the family out of courtesy, and then they will be expected to find other service providers. Eventually, everything we provided will be replaced by our nearest competitors in every aspect. This is the fundamental strength of free systems based on mutual self interest. Losses are temporary events.

Worse yet, some people might be better off. The whole world might be better off if some people are lost. Say I and another man are the only two widget factory owners in town. Say that I bite it and he is now able to grow his business because of the boon of my sudden loss. This isn’t to say he is a bad person; he didn’t plan anything that led to my death. He is even a very good man, perhaps. He is just lucky due to my misfortune, or at the very least, inevitability being that eventually, we are not long for this Earth, regardless. If we consider the last example, though, owning both factories might make him able to achieve marvelous economies of scale, reducing the price of his goods and bettering the widget economy for all now that he is able to do more as the only player than if the two of us competed for limited resources. Maybe this growth will allow him to grow the local economy greatly built on the boom in one company’s widget success. I’ll beat you to the punch, yes I concede there is a possibility the world might be better off if I were dead. My wife, mom and dog would be very sad, but the rest of the world moved on without me and, in this example, were better off for it. Of course, just as easily, that other guy could become a tyrannical monopoly on widgets and you will all cry for the good old days of me. Who is to say?

And that is why we can’t measure human life as a factor. Who is to say what value it has. Was not bin Laden a human life? Did the world gain or lose when the Americans finally tracked him down in Pakistan and relieve the Earth of his presence? Did the world equally gain or lose when my friend Haytak was killed in Iraq? Was one more valuable than the other? Why? What of any individual human who is lost? What of great people? Mao, Stalin, Hitler? Were their deaths a gain or loss to the world? Gandhi, Martin Luther King, or Abraham Lincoln; by what value do we attribute their individual losses? How do any of these compare? Why can we say some losses are good while others are tragic? We cannot. The truth is, the loss of some people greatly disrupts the order and fundamental connections of so many others, damaging the prosperity and happiness of millions. Some of these people, just so happen to be evil. Some other people, very good people, bring about conflict just because they exist. Who is to say the world would be better off, or even worse off, if they suddenly weren’t a part of the picture any more?

Having said all this and tabling the philosophical moral discussions, there is no plausible case that a true zero-sum exchange will ever happen. Some resources will be exchanged and in the immediate event, many will be lost in the war. In the short term a negative-sum event will have occurred. I have yet to see a war which hasn’t ended this way. In the long term though, there have been nations which rebuilt stronger than before because of military conflict. Perhaps it was due to a benevolent ruler or, in the most likely case, the nature of people to take advantage of opportunity when there are gains to be made through efficiencies of scale and new resource interconnectedness. Such an event achieves greater gains than either nation could have achieved on their own assuming there is no change in the level of diplomacy between the two. That said, there is also a third possibility, one where two equally powerful nations duel in such a struggle, that all parties involved are sent back decades. In such an event there is no gain to be had, but a long arduous road back to zero. In such a conflict, the goal is not attempting to maximize gains, but defeat the enemy fast enough that your own losses are minimized. There is also the possibility of disruption, where one nation gains nothing, but utterly destroys, or at least sets another. This too is often the case.

With all this in mind, there can be many outcomes to war, particularly if viewed in the long run. Many negative, but not always. Sometimes there is growth. What there is not, is a case where a conflict arises, and an equal gain is made from an equal loss. Someone out there, values what you have more than you do.

Thanks for reading!

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