Author: Vilen Milner

The vervet monkey, upon encountering a predator, will scream to warn it’s neighbors that danger is nearby, at the cost of attracting more dangerous attention to itself. At first glance, it would seem that natural selection should have wiped out the screaming monkeys from the gene pool. After all, If the monkey remains silent and concentrates on getting itself to safety, it lives on and can spread it’s genes, which it cannot do if it is mauled by the predator. The opposite is the case however, and these monkeys cooperate and work together to survive, why?

Vampire bats also act in a way that at first seems counter-intuitive: the bat can share some of its food with members that were unsuccessful in finding any. This can be modeled in a similar way as the prisoner’s dilemma:

While it makes sense to not warn other members of the species or not share food playing a single game, when you play the same game multiple times the dominant strategy can change.

In the 1970’s, Robert Axelrod, a political scientist, held a tournament which consisted of a fixed number N iterations of the prisoner’s dilemma. Contestants would submit their algorithm that would be a “player”, and at each step the algorithm could only make 1 of 2 choices. The algorithm would have access to previous moves made (a memory), and the goal is to get the highest payoff. The format of the tournament was round-robin, so every player played against each other. The winning algorithm was the simplest one, called tit-for-tat, which consisted of mimicking whatever the opponent did on the previous step. This means that if the opponent decides to be greedy, on the next iteration the player would also be greedy, and if the opponent cooperates, then on the next iteration the player cooperates too. This was the best strategy to ensure the largest payoff.

Perhaps now it is not so difficult to see why members of some species choose to cooperate. If each animal considers each game as a single instance, then they will always choose the greedy approach and end up with a smaller overall payoff. However, by remembering and copying what the others do, cooperation is followed with more cooperation, and the entire species enjoys a higher payoff.

https://www.quantamagazine.org/game-theory-explains-how-cooperation-evolved-20150212/

An interesting article posted in June of 2018 indicates that the power law can be observed in a number of forms of media, with some displaying a steeper curve than others. It is interesting to observe these distributions that can be modelled with math exist in the real world. For example, observe how steep the graph showing success of video game publishers is:

The success of video game publishers is measured by their total global sales, and it is clear that that a select few have lots of success while the rest have very little. In comparison, other forms of media are not as punishing to those less successful, like with song artists:

The curve here is far less steep, indicating that it is easier to get one of your songs to stay on the Billboard Hot-100 for a couple weeks than it is to be a successful video game publisher.

The article also discusses the 80-20 rule, also knows as the Pareto Principle, and looks at how much success the top 20% of entries for each industry have.

It should be noticed that these numbers are related to the steepness of the graph, as one can see that the top 20% of game publishers own 97.69% of all the success in the industry, hence the extremely steep curve. On the other hand, the top 20% of songs only hold 38.88% of the overall song success. It was no accident that I chose those two specific charts earlier in the article. In fact, the tail of the songs chart actually does not follow the power law, which make it even more interesting that out of all the forms of measuring success in the media industry, the number of weeks a song stays on the Billboard Hot-100 is the only one to not follow the power law distribution. Some industries also follow the 80-20 rule very closely, such as success of movie directors:

This curve looks far more like what I expect to see when I think of the power law.

This obviously relates to the entire discussion of the power law from lecture as well as whether or not success depends on simply being lucky or being first, as the information above would suggest that early success is very important in the world of media, although less important for songs than it is for video game publishers.

I chose to write about this article because most of what we see in today’s world is a product of the media industry, and so I thought it was interesting to see how closely success in this industry follows the power law distribution, as likely no movie director or book author is thinking about it when creating their work, and yet it shows up anyways. We were shown an example of this in class with the experiment carried out, but this is a far more recent look of the topic, and I thought it was worthwhile to post.

https://medium.com/@michaeltauberg/power-law-in-popular-media-7d7efef3fb7c