The game theory literature suggests that reasonable actors, under most realistic circumstances, always have better options than to go to war. Yet wars still happen. Why?
I think taking "relative power" rather than resource bargaining as the relevant variable makes things clearer - and explains a decent subset of rational wars.
In a multi-polar world, two warring factions can lose both power and resources by going to war. If the Elven and Dwarven kingdoms are, say, beset by Undead hordes from the North, it may indeed be irrational of them to go to a costly war with each other, because both actors' power relative to the external threat diminishes.
But my sense is that, if there are no real external threats (either because one party is a superpower, or two tribes are fighting over an isolated pacific island), war can be better modelled as a zero-sum game for relative power than a negative-sum game for resources. The destruction of rival political factions is usually a very rational end in itself! Short term resource loss becomes less relevant, and a victor ends the war with far greater political power, which will give incredible pay-offs across generations!
Also, (a novel take, maybe) perhaps this combines with biases/irrational factors (survivorship bias) - most countries have a history of a glorious, successful, more zero-sum war with generational pay-offs (because this tends to be how countries get made), so they presume that future wars may have a similar payoff.
I'm worried that the "relative power" angle takes the "game" part of game theory a bit too literally. Like in a game of Civilization (or, in keeping with the fantasy theme, Smallville) the only check on your desire for power are other states/third parties.
So even a 0.01% chance of winning is better than a guaranteed loss of surrendering your territory.
But in real life, as long as you have literally any other goal than relative power, it behooves you to look for peaceful solutions to pursue them, if you know for sure (or with high probability) that you'd lose a war for sure. Perhaps the elves would prefer being subjugated to the Dwarven Empire to total eradication, or they'd rather be exiles, for example.
I think another type of preferences that can lead to war is just strong preferences? Like, liberal democratic country can attack "Nazi Human Sacrifice Slavery" country just because Nazi Slavers Sacrificing Humans are just that bad and also don't want to give up their lifestyle
Hmm Fearon might describe this as an "indivisible issue", though it's still not clear to me why the Nazi Slavers Sacrificing Humans won't be willing to give up key elements of their lifestyle in exchange for their autonomy, if the alternative is annihilation of their state/being "liberated."
Lovely post that provides a very good review of all the issues and possible failure modes. Thanks so much for putting together such a good explainer.
I mostly agree with everything you say here but just flagging some points where we might disagree. You are probably correct that irrationality in general generally gets too much attention, but I think the specific case of rational irrationality has the opposite problem of getting insufficient attention. At least I have generally not encountered that many discussions of long-term reputation management through war, although in fairness that partially because most actors aren’t quite that long-term oriented. Still while the unwillingness of any nation to consider peacefully giving up territory as part of a bargain has resulted in quite a few pointless wars, it is also certainly the case that this results in international boundaries being respected far more than they would otherwise be, it would be hard to tell whether this is a good thing on balance or not, but it’s an angle that’s often neglected in game theory discussions.
Regarding weapons of mass destruction, there is actually one mechanism that I can think of which causes more war because of them. The mechanism in question is that they reduce the risk of proxy war between Great powers escalating into full conflict, which makes these conflicts safer for the great powers involved and thus reduce the incentive against them. Of course, the increased cost of escalation might be so great that the reduced probability does not make up for it, but just wanted to flag this possibility. As an empirical matter, it does seem that my concern is outweighed by other factors, although it’s hard to tell from just eighty years of history.
As you already noted yourself, some of these failure modes make each other worse like how the fact that you know some irrational actors exist makes information asymmetries worse.
Also, as a cultural factor, unreasonable preferences appear to be declining, although I think human psychology means they will remain a major force but compare to the middle ages elites no longer consider marshal glory, anywhere near as important. Of course, military victory will almost certainly always bring prestige, but I think it does quite a bit less in modern societies compare to the past. Some unreasonable preferences like an unwillingness to permanently split the country instead of fighting and extended civil war or refuse to surrender to sufficiently brutal terms. Even if it’ll just make things worse, are deeply rooted in human psychology, although there are exceptions to even these but other unreasonable preferences are more cultural and appear to be in decline. Mind you nationalism as a modern phenomenon has probably made some unreasonable preferences around national sovereignty and territorial boundaries. More significant, but on balance. I think it’s clear that unreasonable preferences are less of a concern now than they have ever been in the past.
Overall, this was a fantastic post and a marvelous read. Thanks so much for writing it.
This analysis seems to use a fairly simple model of game theory that treats a single war in isolation and assumes each actor just wants the best outcomes from a single interaction. In reality, I think an iterated game is a better model here, from which perspective imposing huge costs (especially nonmonetary costs like lives) on the enemy is an important feature not a bug. If a nation develops a reputation of negotiating bloodless peaces to (for example) sacrifice some land/resources under their control each time a militarily superior power threatens them with invasion, they are much more likely to be invaded in the future compared to developing a reputation for fighting brutally to the last man.
I think this implies that the negotiated peace would (at least for the invader) be fairly bloody for the defender to accept it, which is both politically unpalatable and still results in lots of destroyed resources.
If you apply a more sophisticated timeless decision theory, this also extends to scenarios where the two specific states don't necessarily play repeated games of war, but are part of a larger international community that does.
The Louis XIV example is self-defeating in that Louis himself was not renowned for his constrained and rational foreign policy. France was at war for thirty years or more during his long, long reign. Litigating who is at fault for that would be tedious, but it's certain that his assertive approach to pressing his dynasty's claims in Spain and elsewhere cost France immensely in blood and treasure. Frederick the Great (as you discuss) and Napoleon also immediately come to mind as unchecked absolutists who preferred war to negotiation, though Frederick really spent his whole life defending his initial youthful conquest of Silesia.
I'm not too familiar with the underlying theory but the Bargaining Puzzle feels unconvincing to me. In wars of conquest, the value of the territory shouldn't be modelled as a flat sum of money. It is a rent. In the best case where you conquer and assimilate the disputed territory, you have lost a considerable amount of resources up front, but you will continue to extract that rent until someone takes the territory off you. Securing these rents can permanently alter the trajectory of your nation. Frederick II conquered Silesia and somehow held it against all comers. This strikes me as historically important for Prussia's escape from an unstable position as one power of many in Germany to the rank as of Europe's leading powers. After a challenging period during the Napoleonic era (and they were not alone in that), Prussia led on the project of German unification and managed to exclude Austria, with historic consequences for the twentieth century. It's hard to imagine this would be possible without Frederick's victories in the eighteenth century.
Not only does conquering a territory gain you rent, it denies that rent to your strategic rivals, materially weakening them in future conflicts. This affords you the opportunity to come back for more later, once you have paid off the debt paid in conquering the disputed territory using that territory's resources. I think this is part of Putin's thinking in Ukraine, though it is probable he miscalculated the costs involved in these wars of conquest.
I agree that wars of conquest are rather unfashionable now for many of the reasons you discuss, but I am not convinced of their intrinsic irrationality.
I mean the big one is that it makes your future promises non-credible, so doing this forecloses the possibility of future deals with other state actors, as long as the private benefits of deal-breaking are sufficiently large.
The expenditure of credibility is real, but their loss of credibility won't bring back your lost territory unless a third party intervenes. And nations can always mask their perfidy with a cloud of diplomatic verbiage and false-flag action. It is not difficult to imagine the results of Ukraine giving Russia a large sum of money in lieu of territory in the Donbas before the recent conflict.
If war is irrational because a bargain is always possible in spherical cow universe, but bargains are impossible in the universe actual humans live in, can we really say that war is irrational?
I believe that paying an aggressor to go away is a fundamentally flawed strategy, for reasons that are obvious to most people most of the time. Sometimes it is your best try, and occasionally it will even work, but it is easy to exploit.
If the elves conclude that the dwarves will win a war, and offer them tribute to go away, that action itself influences the balance of forces. The elves are weaker by the sum of the tribute, and the dwarves are that much stronger. Consider the psychological consequences of admitting you are the weaker party for all the world to see, and the gap is likely to grow even wider. The dwarves can go back for more, and the logic of the bargain dictates they are offered an even better deal to reflect their improved position. This is a strong incentive for defection and predation.
Principal-agent problems can go the other way as well; it's not only a leader that can personally benefit from a war. For example, a subordinate military officer - or even an individual soldier - might be in a position to personally benefit more from success in war than they could by simply showing up and collecting tribute, and therefore might be inclined to start trouble whether their own bosses want them to or not.
Rudyard Kipling wrote a famous poem about the problem of a lack of a commitment mechanism.
https://en.wikisource.org/wiki/Rudyard_Kipling%27s_Verse,_Inclusive_Edition,_1885-1918/Danegeld
I think taking "relative power" rather than resource bargaining as the relevant variable makes things clearer - and explains a decent subset of rational wars.
In a multi-polar world, two warring factions can lose both power and resources by going to war. If the Elven and Dwarven kingdoms are, say, beset by Undead hordes from the North, it may indeed be irrational of them to go to a costly war with each other, because both actors' power relative to the external threat diminishes.
But my sense is that, if there are no real external threats (either because one party is a superpower, or two tribes are fighting over an isolated pacific island), war can be better modelled as a zero-sum game for relative power than a negative-sum game for resources. The destruction of rival political factions is usually a very rational end in itself! Short term resource loss becomes less relevant, and a victor ends the war with far greater political power, which will give incredible pay-offs across generations!
Also, (a novel take, maybe) perhaps this combines with biases/irrational factors (survivorship bias) - most countries have a history of a glorious, successful, more zero-sum war with generational pay-offs (because this tends to be how countries get made), so they presume that future wars may have a similar payoff.
I'm worried that the "relative power" angle takes the "game" part of game theory a bit too literally. Like in a game of Civilization (or, in keeping with the fantasy theme, Smallville) the only check on your desire for power are other states/third parties.
So even a 0.01% chance of winning is better than a guaranteed loss of surrendering your territory.
But in real life, as long as you have literally any other goal than relative power, it behooves you to look for peaceful solutions to pursue them, if you know for sure (or with high probability) that you'd lose a war for sure. Perhaps the elves would prefer being subjugated to the Dwarven Empire to total eradication, or they'd rather be exiles, for example.
the survivorship bias thing is interesting! I should consider it more.
I think another type of preferences that can lead to war is just strong preferences? Like, liberal democratic country can attack "Nazi Human Sacrifice Slavery" country just because Nazi Slavers Sacrificing Humans are just that bad and also don't want to give up their lifestyle
Hmm Fearon might describe this as an "indivisible issue", though it's still not clear to me why the Nazi Slavers Sacrificing Humans won't be willing to give up key elements of their lifestyle in exchange for their autonomy, if the alternative is annihilation of their state/being "liberated."
Lovely post that provides a very good review of all the issues and possible failure modes. Thanks so much for putting together such a good explainer.
I mostly agree with everything you say here but just flagging some points where we might disagree. You are probably correct that irrationality in general generally gets too much attention, but I think the specific case of rational irrationality has the opposite problem of getting insufficient attention. At least I have generally not encountered that many discussions of long-term reputation management through war, although in fairness that partially because most actors aren’t quite that long-term oriented. Still while the unwillingness of any nation to consider peacefully giving up territory as part of a bargain has resulted in quite a few pointless wars, it is also certainly the case that this results in international boundaries being respected far more than they would otherwise be, it would be hard to tell whether this is a good thing on balance or not, but it’s an angle that’s often neglected in game theory discussions.
Regarding weapons of mass destruction, there is actually one mechanism that I can think of which causes more war because of them. The mechanism in question is that they reduce the risk of proxy war between Great powers escalating into full conflict, which makes these conflicts safer for the great powers involved and thus reduce the incentive against them. Of course, the increased cost of escalation might be so great that the reduced probability does not make up for it, but just wanted to flag this possibility. As an empirical matter, it does seem that my concern is outweighed by other factors, although it’s hard to tell from just eighty years of history.
As you already noted yourself, some of these failure modes make each other worse like how the fact that you know some irrational actors exist makes information asymmetries worse.
Also, as a cultural factor, unreasonable preferences appear to be declining, although I think human psychology means they will remain a major force but compare to the middle ages elites no longer consider marshal glory, anywhere near as important. Of course, military victory will almost certainly always bring prestige, but I think it does quite a bit less in modern societies compare to the past. Some unreasonable preferences like an unwillingness to permanently split the country instead of fighting and extended civil war or refuse to surrender to sufficiently brutal terms. Even if it’ll just make things worse, are deeply rooted in human psychology, although there are exceptions to even these but other unreasonable preferences are more cultural and appear to be in decline. Mind you nationalism as a modern phenomenon has probably made some unreasonable preferences around national sovereignty and territorial boundaries. More significant, but on balance. I think it’s clear that unreasonable preferences are less of a concern now than they have ever been in the past.
Overall, this was a fantastic post and a marvelous read. Thanks so much for writing it.
This analysis seems to use a fairly simple model of game theory that treats a single war in isolation and assumes each actor just wants the best outcomes from a single interaction. In reality, I think an iterated game is a better model here, from which perspective imposing huge costs (especially nonmonetary costs like lives) on the enemy is an important feature not a bug. If a nation develops a reputation of negotiating bloodless peaces to (for example) sacrifice some land/resources under their control each time a militarily superior power threatens them with invasion, they are much more likely to be invaded in the future compared to developing a reputation for fighting brutally to the last man.
I think this implies that the negotiated peace would (at least for the invader) be fairly bloody for the defender to accept it, which is both politically unpalatable and still results in lots of destroyed resources.
If you apply a more sophisticated timeless decision theory, this also extends to scenarios where the two specific states don't necessarily play repeated games of war, but are part of a larger international community that does.
The Louis XIV example is self-defeating in that Louis himself was not renowned for his constrained and rational foreign policy. France was at war for thirty years or more during his long, long reign. Litigating who is at fault for that would be tedious, but it's certain that his assertive approach to pressing his dynasty's claims in Spain and elsewhere cost France immensely in blood and treasure. Frederick the Great (as you discuss) and Napoleon also immediately come to mind as unchecked absolutists who preferred war to negotiation, though Frederick really spent his whole life defending his initial youthful conquest of Silesia.
I'm not too familiar with the underlying theory but the Bargaining Puzzle feels unconvincing to me. In wars of conquest, the value of the territory shouldn't be modelled as a flat sum of money. It is a rent. In the best case where you conquer and assimilate the disputed territory, you have lost a considerable amount of resources up front, but you will continue to extract that rent until someone takes the territory off you. Securing these rents can permanently alter the trajectory of your nation. Frederick II conquered Silesia and somehow held it against all comers. This strikes me as historically important for Prussia's escape from an unstable position as one power of many in Germany to the rank as of Europe's leading powers. After a challenging period during the Napoleonic era (and they were not alone in that), Prussia led on the project of German unification and managed to exclude Austria, with historic consequences for the twentieth century. It's hard to imagine this would be possible without Frederick's victories in the eighteenth century.
Not only does conquering a territory gain you rent, it denies that rent to your strategic rivals, materially weakening them in future conflicts. This affords you the opportunity to come back for more later, once you have paid off the debt paid in conquering the disputed territory using that territory's resources. I think this is part of Putin's thinking in Ukraine, though it is probable he miscalculated the costs involved in these wars of conquest.
I agree that wars of conquest are rather unfashionable now for many of the reasons you discuss, but I am not convinced of their intrinsic irrationality.
rent is not worth infinitely more than a lump sum! There's a simple and natural equivalence between the two via Net Present Value!
Is there anything stopping the probable victor from taking the lump sum and using it to help pay for the conquest of the rent?
I mean the big one is that it makes your future promises non-credible, so doing this forecloses the possibility of future deals with other state actors, as long as the private benefits of deal-breaking are sufficiently large.
But otherwise it reduces to Commitment Problems/Noncredible Commitments, discussed above (https://linch.substack.com/i/172819064/the-shadow-of-the-future-incredible-commitments).
The expenditure of credibility is real, but their loss of credibility won't bring back your lost territory unless a third party intervenes. And nations can always mask their perfidy with a cloud of diplomatic verbiage and false-flag action. It is not difficult to imagine the results of Ukraine giving Russia a large sum of money in lieu of territory in the Donbas before the recent conflict.
If war is irrational because a bargain is always possible in spherical cow universe, but bargains are impossible in the universe actual humans live in, can we really say that war is irrational?
Do you actually believe bargains are impossible in our existing universe?
I believe that paying an aggressor to go away is a fundamentally flawed strategy, for reasons that are obvious to most people most of the time. Sometimes it is your best try, and occasionally it will even work, but it is easy to exploit.
If the elves conclude that the dwarves will win a war, and offer them tribute to go away, that action itself influences the balance of forces. The elves are weaker by the sum of the tribute, and the dwarves are that much stronger. Consider the psychological consequences of admitting you are the weaker party for all the world to see, and the gap is likely to grow even wider. The dwarves can go back for more, and the logic of the bargain dictates they are offered an even better deal to reflect their improved position. This is a strong incentive for defection and predation.
Principal-agent problems can go the other way as well; it's not only a leader that can personally benefit from a war. For example, a subordinate military officer - or even an individual soldier - might be in a position to personally benefit more from success in war than they could by simply showing up and collecting tribute, and therefore might be inclined to start trouble whether their own bosses want them to or not.
Yes arguably this happened a number of times in the IJA during WWII