This post is on Evolutionary Game Theory, derived from the book Networks, Crowds and Markets: Reasoning about a highly connected world by David Easley and Jon Kleinberg. This seemingly esoteric field shines a light on an incredible number of things, including evolution, wars, and society itself. Although the subject is inherently mathematical, the mathematics only serves to distract from the ultimate message in a lot of examples. Hence, this article mostly avoids formulae and lengthy calculations. Almost all the examples constructed in this article are my own.
What does Game theory actually mean? Imagine that India and Pakistan are about to go to war. Both sides have declared the other to be responsible for recent provocations, and have justified to their citizens the use of overwhelming force to crush the enemy. Who should attack first? Should they attack at all?
If both of them are able to stop themselves from going to war, both of them will benefit. No soldiers or citizens killed, no blow to the economy, you name it. However, if one of them surprise attacks first, they will catch the other sleeping and quickly be able to gain territory. This will boost the economy, and improve public morale, ensuring that the current government surely wins the next election. Hence, the benefits of attacking first outweigh the benefits of withholding from attack in this situation.
If India and Pakistan are not in communication with each other, they will each expect that the other will want to attack first. Hence, if only to preemptively deny this advantage to the other, they will both attack, leading to entrenched warfare, massive destruction, with very little gain.
If one could quantify the benefits of going to war or abstaining from war in a table, it would look something like this:
Hence, if India and Pakistan are not in communication with each other, out of sheer insecurity, they will attack each other, leading to a bad result in which both of them suffer. However, if they are in communication with each other, and show cooperation by agreeing not to attack one another, they will both avoid a whole lot of damage and suffering.
This is an example of the classic Prisoner’s Dilemma, in which insecurity amongst people leads to bad conclusions. If I take pains to help out a classmate who will never help me in return, then without communication I will just assume that I’m being a fool, and that I might as well be unhelpful to that person. This inevitably leads to an uncomfortable atmosphere in class for both. However, if both of us have a verbal or non-verbal understanding that we will always help the other out, then both of us can benefit. Life is generally not a zero-sum game, and humans generally do benefit from cooperation, as long as they play by the rules.
Game theory is the study of decision making in such circumstances.
Evolution, as we all know, is the process through which some genetic traits persist over time, while others are wiped out. If there are two types of owls on an island, identical in every way except for the fact that one type is blind and the other can see, then soon enough the blind owls will be wiped out from the island. This is because it will be in direct competition with the seeing owls for food and other resources. How did one type of owl come to be blind while the other did not? Most genetic differences arise because of random mutation. It is possible that owls were always blind, and due to a random mutation one of them could see. This mutated owl cold hunt better, and soon gave birth to a lot of kids who also had eyes. Gradually, these owls with the power of vision out-competed the “original” blind owls, established their dominance over the island, and with a couple of hundred years those blind owls were nowhere to be found.
Note that evolution is the composite of random mutation and natural selection. It is not the process through which one species naturally dominates another. For instance, when humans first reached Australia more than 40,000 years ago, they hunted many species into extinction. This is not explained through evolution. Evolution only occurs gradually between members of the same species that are distinct only in small ways, their differences caused by random mutation.
Evolutionary Game Theory
How does game theory come into the picture though? Let us suppose that in a large community of say a thousand pigs, ten pigs have three legs instead of four due to random mutation. What will happen? The other pigs will out-compete these mutated pigs for food, shelter and mates. These mutated pigs will probably starve a lot of the time, not have many mates, and hence much fewer children than the rest. The fraction of three-legged pigs will slowly decrease generation upon generation, until it is negligible (or even zero). A genetic trait is called evolutionarily stable if a large enough fraction of the population with that trait can successfully dominate all other mutations, provided that the fraction of such mutants is small enough. Having four legs seems to be an evolutionarily stable trait. Of course we haven’t proved it yet. What if even one pig with 16 legs can out-compete this pig population for food and mates? This is unlikely, as this 16 legged pig will only be made fun of by the others, and will find it hard to attract mates in order to pro-create. Hence, in all likelihood, having 4 legs is evolutionarily stable for this population of pigs.
Let us take another example. Imagine that in a society with a thousand humans, one socially awkward child with a super high IQ is born. If there is only one such child, he/she will struggle to fit in, probably fail to attract mates in competition with others, and hence this mutation will die out. Hence, average IQ is evolutionarily stable, and not a very high one. However, if a sufficiently large number of children are high IQ mutants, they can fend for each other, procreate with each other, and ultimately beat others while in competition for limited resources. Hence, high IQ can spread only if the number of high IQ mutants is large enough to begin with. This would perhaps explain the current state of the world to some extent.
But what happens if the world is mostly comprised of high IQ individuals, and a small number of low IQ mutant is introduced? Intense competition between the high IQ individuals may lead to their mutual destruction. For example, two technologically advanced nations may blow each other up with nuclear weapons, while less advanced nations may survive unscathed. In the aftermath of this destruction, the low IQ mutants may pro-create comfortably, soon populating society with mostly low IQ individuals. Hence, high IQ is not evolutionarily stable.
In the book Sapiens by Yuval Noah Harari, the author argues that Neanderthals were known to actually have a bigger brain than Homo sapiens, and a bigger brain generally translates to a higher IQ. Hence, it was always a mystery how Sapiens managed to exterminate the Neanderthals and spread over the whole world. Perhaps the fact that high IQ is not evolutionarily stable explains this counter-intuitive phenomenon.
What is Nash equilibrium? It is an arrangement between two players in which neither side will gain from changing their strategy. For example, let us suppose that India and Pakistan agree to not go to war with each other. If Pakistan now changes its stance and attacks India, India will retaliate by attacking Pakistan. In this way, things will only become worse if either country stances its stance from peace to war. This shows that both countries being at peace is a Nash equilibrium.
What does Nash equilibrium have to do with evolution? Things that are evolutionarily stable are also Nash equilibria. What this means is the following: suppose we have a population with an evolutionarily stable trait (say, average IQ). If a small fraction of individuals suddenly becomes high IQ, that small fraction will soon be wiped out. Hence, when two average IQ persons are competing for a resource, it will not benefit either of them (over the long run) to become a high IQ mutant. Hence, the only stable arrangement, in which everyone is well-off over the long run, is if everyone has an average IQ.
In some situations, we don’t have an evolutionarily stable trait.
Consider the scenario in which most countries of the world are peaceful and minding their own business. Suddenly, the US starts attacking everybody, soon accumulating a load of wealth and territory. Other countries will soon follow suit, and the world will descend into chaos. But in this aftermath of bloody destruction, people will realize that Switzerland has remained unscathed because it refused to descend into this horrible mess. They will realize their folly, and decide to again become peaceful. Soon, most countries in the world are again peaceful. But then they see Russia attacking countries near its borders, slowly gaining control over large parts of the world. To prevent the scaled from being tilted too heavily in Russia’s favor, other countries soon join the fray.
In this way, much of world history has been a story of wars, interspersed with periods of genuine peace. Neither war, nor peace are evolutionarily stable. It took only one belligerent country to make all other countries go to war, and it took only one peaceful, relatively unscathed country to make everyone return to peace. I don’t mean to overplay my hand, but this could be a possible reason why humanity has often oscillated between wars and peace, and neither has stuck.
What should one do then? The author of the article proposes that we should have a mixed strategy in situations without pure evolutionary equilibria. What would that look like in this situation? Suppose all countries mutually decide to initiate an attack with another only one time out of ten (of course all countries can retaliate every time they’re attacked first). If a country suddenly starts attacking everyone, it will find itself always at war, its people and economy destroyed. Hence, it will adapt to attacking less frequently. If a country that is involved in world politics never initiates an attack, it will soon enough find itself attacked first by another country, and will hence suffer considerable damage. Soon, it will start initiating some attacks on its own to never let the past repeat itself. Hence, attacking sometimes, perhaps one time out of ten, is the evolutionarily stable strategy, as eventually everyone will start doing this.
As one may imagine, game theory can probably be applied almost everywhere in human life. When people lack cooperation, insecurity ultimately leads them to destroy their own peace of mind and others’. For example, in a society in which everyone throws garbage on the roads, one person deciding not to do so and taking pains to clean the streets is at a disadvantage. Other people will keep throwing garbage on the streets. Hence, that person will soon decide to stop his/her futile efforts, and litter the streets like other. This shows that the situation in which everyone throws garbage on the streets is evolutionarily stable. However, if people cooperate and mutually decide to never throw garbage on the streets, and also to punish/fine individuals that pollute the streets, our streets will remain clean forever. Hence, clean streets can be evolutionarily stable only when people communicate and cooperate with each other. I stole this example from the book Algorithms to Live By, by Brian Christian and Tom Griffiths. This book also re-kindled my desire to finally understand Game theory, after multiple failed attempts in the past.
- Evolutionary Game Theory, by Easley and Kleinberg