The Origins of Game Theory: Evolution, Adaptation, and Strategy Through the Ages

Introduction

Human beings are social animals; through the process of evolution, mankind developed short-term tactics and long-term strategies in order to cooperate and exist together in a society and, in turn, a civilization.

Game Theory is a branch of applied mathematics that uses models of strategic interactions where subjects or players make decisions that are interdependent. It is used to study decision making of animals, humans, and even computers. It was first developed by John Von Neumann and Oskar Morgenstern in 1944.

In this blog, we are going to discuss the basic concepts of Game Theory with some popular examples, and also understand how decision-making and strategy evolved from the genetic or individual level to society to the civilizational level.

Chapter 1 – The Game Theory Primer: Models of conflict & cooperation

The Prisoner’s Dilemma-

Let us suppose two people, A and B, have been caught as suspects for a crime, but the police have no hard evidence. So they took the two prisoners separately and gave them a choice- either to confess or not, with the condition that- 

i. If both confess, they get deserved punishment, but on early parole, let it be 2 years.

ii. If one confesses and the other denies, the one confessing is set free, let it be 0 years, and the other gets a harsher punishment, let it be 3 years.

iii. If both deny, both are given even lighter punishment, as the police have no hard proof to give the actual punishment, let it be 1 year.

So the condition that arises can be described in tabular form as this.

	B stays silent	B confesses
A stays silent	1,1	3,0
A confesses	0,3	2,2

Now, A does not know what B will choose. Suppose B stays silent, A will suffer less if he confesses, as 0 years are better than 1 year. Now, if B confesses, A will suffer less if he confesses because 2 years are better than 3 years.

The same is also true from B’s point of view.

Thus, both of them confess to making the best decision.

This is the non-iterative form of the prisoner’s dilemma, that is, they don’t have to repeat the same thing again.

Now, if the Prisoner’s Dilemma is repeated-

To see this, Robert Axelrod, a political scientist, organized a computer game tournament in 1980. He invited many game theorists to participate in the tournament with their own unique programs, which were called strategies. In the tournament, each strategy was paired with another for a 200-round Prisoner’s Dilemma game. The whole tournament was repeated 5 times to make it precise. A total of 15 strategies participated, and the winner was a strategy called “ tit for tat”. It was designed such that it cooperated at first but defected once after its opponent defected, that is, it held a grudge only for the next round and then forgave. 

All the top top strategies shared some qualities-

1. They were nice and didn’t defect at first.
2. They were forgiving and didn’t hold a grudge after 1 round.

Then Alexrod organized a second tournament, with the only change being that no one knew the actual number of rounds. That time, a total of 63 strategies participated. The winner was again “tit for tat”.

Apart from the first two qualities, Axelrod found two more qualities in top strategies-

3. They retaliated immediately in the next round after being cheated.
4. They were clear and simple.

Although when tit for tat was later run against all nasty and defecting strategies, it came last, which shows there is no single best strategy; everything depends on the situation and surroundings. Although it was also seen that when there was some cooperation from other strategies, tit for tat and other good strategies, although being a minority, became dominant strategies soon. Later, it was found that tit for tat would do better if it retaliated 90% of the time instead of 100%. 

Zero-Sum vs Non-Zero-Sum Games

Zero-Sum games are those where one person’s win is another person’s loss. For example, tennis, chess, and most sports.

Non-Zero-Sum games or strategies where one person’s outcome is independent of the other’s and vice versa. For Example- If there are two shops and only one customer, if he goes to one shop doesn’t mean a loss to the other shop, as he can go there too at a later time; in fact, he has neither gained nor lost anything.

I would like to refer to Veritasium’s YouTube video titled “What Game Theory Reveals About Conflict and War” if anyone wants more details.

Chapter 2- Evolution of Strategies at the Genetic and Individual Level

The concept of Evolution in its true form was first described by Charles Darwin around 1859. Although before him many have inkings to the truth, it was Darwin who gave a structured theory to it. It is the evolution of strategies at the genetic level that helped us survive for millions of years. Each species has developed unique strategies to survive with its own set of morals. Black-headed gulls eat each other’s babies, and female Praying Mantises eat their male partners during mating for nutrition. Bees defend their nests/hives by stinging and, in turn, sacrificing their lives. Each organism has its own strategy, mostly to survive and pass on its genes.

The more they replicate, the more the species survives. DNA acts as our replicator for survival. The British evolutionary biologist Richard Dawkins, in his book “The Selfish Gene,” suggests that it is more natural to be selfish than to be altruistic in order to survive.

Now, let us consider a Hawk and a Dove interaction and assign points to the results-

50 points for a win, 0 for a loss, -100 for being seriously injured, and -10 for wasting time over a long contest. These points can be thought of as being directly convertible into the currency of gene survival.

In a single Hawk vs Dove interaction, Hawk will always win. If there are only Doves, the winner will get 50 points for winning and -10 for wasting time, so in total, he scores 40. The loser gets -10 for wasting time, so the total average payoff from this interaction is  (40-10)/2 =15. But now, if a mutant Hawk arrives in the population, he beats every dove and scores 50 each time; he enjoys a huge advantage over the doves, who usually get 15 on average. Hawk’s gene will thus rapidly spread through the population. But slowly the Hawks’ chances to win every fight will decrease, and at last, if there are only Hawks left, the winner will get 50, but the loser will get -100 for being seriously injured, resulting in the average result of interaction (50-100)/2= -25. But now a single Dove moves in the population, he will lose, but he manages to never get hurt, his average payoff is 0, while Hawks are usually getting -25, so Dove’s gene will survive and spread through the population. The stable ratio of Hawks and Doves turns out to be (7/12) and (5/12). At this point, the average pay off of both the Hawks and the Doves is equal to about 6(¼).

This model also applies to human beings. Apart from the Hawk and the Dove strategies, there are other strategies like the Retaliator, which plays like a Dove in the beginning but retaliates when attacked by a Hawk. There is also the Bully who behaves like a Hawk until someone hits back, then he runs away. Another strategy is the Prober-Retaliator, who behaves like a Retaliator but occasionally tries experimental escalation of the contest. He behaves like a Hawk if his opponent does not fight back, and if opponents fight back, he reverts to conventional threatening like a Dove.

Among the five strategies in a computer simulation, the Retaliator emerges as the most stable, followed by Prober-Retaliator, which is nearly stable. Although this result, the implementation of strategies varies from one situation to another.

Each individual has a much closer relationship with individuals with whom they share more genetic information or relatedness. An individual is closer to his parents because he shares 50% genes with both his father and mother, and their relatedness is thus (½). The relatedness between two brothers is also (½) as they share 50% of genes. The formula for relatedness can be written as m*(½)^n, where m is the number of common ancestors, and n is the generational distance. For example, the first cousins have two common ancestors and their generational distance is 4, so the relatedness will be 2*(½)^4=(⅛). Thus, a man is closer to his sibling than his first cousin.

So in this chapter, we see that individuals form groups and associations or act solo based on the strategies of their survival. This chapter also reveals that game theory doesn’t just apply to economics or war- it’s deeply rooted in biology & life.

Chapter 3- Homo sapiens & the Rise of Civilizations

Homo sapiens, or the modern human, arrived on Earth about 300,000 years ago in Africa, and about 150,000 years ago, they began to spread to the rest of the world. Before that, there were many other species of humans living in Afro-Eurasia, such as Homo neanderthalensis and Homo erectus. But around 70,000 years ago, something occurred which made Homo sapiens superior to other human species and slowly drove them extinct- The Cognitive Revolution. Due to this, Homo sapiens developed the art of gossiping and telling stories, which enabled them to form larger groups compared to their counterparts. Imagination and gossip created ideas that continued to live even after the creators were dead. This enabled two individuals with no records of previous encounters to begin working together under a common idea. According to historian Yuval Noah Harari and his book “Sapiens: A Brief History of Humankind”, the Cognitive Revolution is accordingly the point when history declared its independence from biology.

The Cognitive Revolution also enabled Homo sapiens to travel from one place to another in a group in an efficient way; they were the only species of humans to arrive in the New World. The stories they created soon got embedded in their culture, giving rise to myths and religions around which the earliest settlements were made.

Then, around 12,000 years ago, came another important point of human history- the Agricultural Revolution. As a result, human beings weren’t required to live their life as hunter-gatherers and thus began to settle down around rivers or areas suitable for agriculture. This resulted in history’s first towns and cities being formed in areas like the Fertile Crescent, the Nile River Valley, the Indus River Valley, the Yellow River Valley, and around the eastern coasts of the Mediterranean Sea. That was also the time when the domestication of animals like sheep, goats, pigs, and chickens took place.

Early society ran on barter systems of give and take. But it had a problem: to make a trade, each side was required to want what the other had to offer. Thus, money was created as a medium to systematically represent the value of other things for the purpose of exchanging goods & services. The earliest form of money was about 4000 years ago, when shells were used as money. Money soon developed in different regions of the world in different ways, which completely created a new direction for the evolution of mankind.

Another important point in human evolution was the Scientific Revolution and the Age of Discovery around 1500 CE. Before that, the border between philosophy & science was not very clear, and scientific thoughts were mostly dominated by religions & theologies all over the world. Due to the contribution of geniuses like Nicolaus Copernicus, Galileo Galilei, Johannes Kepler & Sir Isaac Newton, a clear process of scientific thinking was invented, which was clearly distinct from philosophical & theological thoughts. This accelerated the progress of scientific studies, which in turn accelerated human evolution. Also, it was the 1500s when explorers & merchants like Christopher Columbus & Vasco da Gama began their journey of exploration and discovered new continents like America & new trade routes like throughthe Cape of Good Hope to India. Both the scientific revolution and the age of discoveries enabled a small continent like Europe to colonize most of the world, which further led to the world we see today.

This chapter thus shows how human beings used storytelling, agriculture, and science to become the ultimate players in the game theory of life.

Chapter 4- The Effect of Nature & Environment on Human Civilizational Strategies

The human societies that developed all around the world were directly affected by the following environmental variables: climate, geological type, availability of resources, area of landmass, terrain, and connectivity. We see that the early civilizations evolved faster around tropical or sub-tropical regions. For example, the Mesopotamian, Egyptian & Indus Valley Civilizations progressed at a faster rate compared to cultures in the Steppes. This was because the former regions get more direct sunlight compared to the latter regions. Since the early economy was agrarian, the places with more sunlight have more developed agriculture & economy. Also, rivers like the Euphrates, Tigris, Nile & Indus played an important role in providing water for irrigation, which the areas like the Arabian Peninsula didn’t receive much. The shape of the landmass also heavily affected the spread of culture and, in turn, growth. Historian Jared Diamond in “Guns, Germs & Steel” states that the cultures in Eurasia evolved faster than the cultures in the Mesoamerica and Sub-Saharan Africa because Asia and Europe are longer in the East-West direction thus the climate being same it was easier to communicate, where as America & Sub-Saharan Africa are longer in the North-South direction which hindered communication because of variation in latitudes and in charge climate.

Also, some countries developed natural protections that protected them from foreign invasion to some extent. For Example, the Himalayas for India, the Tibetan Plateau & the Mongolian Plateau for China & the Sahara Desert for Egypt. This caused those countries to feel secure from early invasions and concentrate on their individual progress. The livestock also played an important role in the cultures, for example, the camel in the case of Egypt & the cow in the case of India.

The ease of communication also got affected by the availability of nearby routes, which are tried & tested, thus the cities on the Silk Route slowly evolved into influential economic hubs.

Later, after scientific & industrial evolutions in the 15th-16th & 18th-19th centuries, different criteria became more important. Colder countries began to develop more as there were easier to store rations, compared to hotter countries. Moreover, the disadvantages due to terrain & isolation disappeared because of the invention of railways, airways, telephones, mobile phones & internet.

In the modern world, the civilizational game theory is less dependent on natural causes & more dependent on scientific, economic, military & political causes.

Conclusion

Thus, we conclude that game theory acts at different levels- genetic, individual, societal, geographic, civilizational, as well as economic & political. In understanding these games, it just won’t help us to understand history but also help us in discovering the hidden causes of genetic, human & civilizational progress.

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Suggested Reading

1. The Selfish Gene by Richard Dawkins
2. Sapiens: A Brief History of Humankind by Yuval Noah Harari
3. Guns, Germs & Steel by Jared Diamond

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