Author: Pin Yao Zhang

Investing comes in many forms, one of the most popular is investing in stocks. Many can get rich in a heartbeat, but many can fall deep into the abyss very quickly as well, because there is no absolutely accurate formulas to derive the future of the market. However, with the use of game theory concepts, the chances of landing a profit in the investment will increase.

Many people will perform many kinds of analysis on the stocks they would like to purchase, but at the very basis of investing, the investors sentiment is the basis of most of the investments in specific stocks. Sentiment is the emotion which the investors feel towards the stock itself and not the company; hence, the investors are trying to predict what majority of the other investors are going to invest in. The more investments made to a particular stock, the higher the price will go, thus more profit for each investor.

Now of course this market doesn’t only consist of one other type of player like the examples showed in lecture, where there are only player A and B, now it consists of a very large amount of players, such as individual investors, governments, corporations, hedge funds, etc. Additionally, there are different kinds of strategies, such as limit buy/sell, shorting or options, to make profits.

Let us set up a scenario as an investor, you would like to buy some stocks of companies you like, and you came across two companies that you have great interest in. Assuming that you are able to accurate predict and formulate this payoff matrix for stock A and B after a year, which one would you choose to buy?

Stock A:

You/others	Buy	Sell
Buy	70, 70	-50, 90
Sell	-50, 90	10, 10

Stock B:

You/others	Buy	Sell
Buy	60, 90	-30, 100
Sell	-30, 100	95, 95

Clearly there is no dominant strategy for either stocks, since we can see that for both stocks, regardless of you buying more after one year or selling after one year depends on what all other people are doing in the market. However, you can use mixed strategy equilibrium to predict which is a better buy. Let p equal to you buying in and q equal to others buying. If you do the calculations, you will get that for stock A, p = 4/5 and q = 1/3, for stock B, you get q = 25/43 and p = 19/21.

Based on these data, you can say that it is better to buy stock B since the probability of other investors buying stock B is larger than the probability of other investors buying stock A (25/43 > 1/3). As stated before, the more people that buys the stock, the higher the stock is valued. Under the circumstance of no dominant strategies exist for both stocks, using mix strategy allows you to have a better forecast on which stock to purchase.

To generate an accurate model of the market’s future is basically impossible, but we can use computers to help us model all different types of scenarios to conclude a set of results that we can use to help while we invest. This simple scenario is just to show that exercising game theory concepts on top of the other analytics one performs when investing will increase the chances of yielding more profit. But keep in mind that the stock market is far more complex and far more unpredictable than any situations.

Citations:

https://www.businessinsider.com/ben-hunt-on-the-sentiment-game-2013-11

https://seekingalpha.com/article/4357662-investing-game-theory

We all made friends throughout our lives, some made more friends, some made less. But do you know that you actually have less friends than you thought you had? Now to illustrate this, think about the friends you have on social media, whether its Facebook, Instagram, Twitter, Wechat, most likely you will realize that you have connections to more people than you actually talk to and consider as friends.

This is based off of the friendship paradox, a form of sampling bias which states friends of a person tends to have more friends than the person thinks. This observation was first talked about in 1991, where a sociologist Scott Feld, conducted a study on social networks of people. His study was to take a deep dive into the average number of friends a person has in their own network and compared it with the average number of friends this person’s friends have. He concluded that the average number of person’s friends is always higher than the average number of friends for this person.

Another example conducted by Young-Ho Eom and Hang-Hyun Jo at Aalto, in which one study they conducted was taking two academic networks, where scientists are linked if they have co-authored papers together. A graph was generated where each node is a scientist and was represented in a paradox holding probability they defined as h (k, x) where k is the degree and x is the node characteristics.

Graph a is a representation of numbers of coauthors, graph b is for the number of citations, graph c is the number of publications and graph d is the average number of citations per publications.

Later on in the study, they conducted using different sampling strategies to see if other sampling methods yield the similar results. Here are the characteristic distributions of the sampled data in the network using different sampling methods.

The common observations from the graphs, which are degree distributions, is that the denser the distributions, the better sampling it implies for the high characteristic nodes. Also, in most cases, the friend sampling shows a better result than random sampling, but one area, which is the average number of citations per publications in the network. As we can see in graph D, that the degree characteristic correlation is very small, around 0.07, but still yields very good results in comparison to other methods.

As expected, looking at a specific scientist and compare it to its co-authors, it reflects the results of the friendship paradox, where the co-authors have more co-authors than the selected scientist. The reason behind this paradox is because of how the graphs are constructed and how the ties between nodes structured.

Do not feel inadequate about “having less friends than your friends”, since most people are actually in similar positions. Just remember friends are all about the quality not the quantity. 

Sources:

ArXiv, E. (2020, April 02). How the Friendship Paradox Makes Your Friends Better Than You Are. Retrieved October 17, 2020, from https://www.technologyreview.com/2014/01/14/174587/how-the-friendship-paradox-makes-your-friends-better-than-you-are/

Eom, Y., & Jo, H. (2014, April 10). Generalized friendship paradox in complex networks: The case of scientific collaboration. Retrieved October 17, 2020, from https://arxiv.org/abs/1401.1458