Author: Guikang Zhong

Game theory is the study of mathematical models on how two entities make decisions against each other so that they are able to get the maximum benefit. This useful theory can explain a lot of phenomena in the marketing including why often small companies have difficulties expanding the market like the huge companies. Game Theory can be used to explain it.

Let’s assume theoretically, there are two companies, one is a big company A and the other one is a small company B . They both find a new product that can be introduced into the market and expand it. The product values 10 million dollars in the market, Here are three situations: 1. A, B expand, earning ratio 7:3. 2. A expands, B wait, earning ratio 6:4. 3. A waits, B expands, earning ratio 9:1. Each expansion cost 2 million dollars. Here is the diagram that shows the profit each company makes in different choices. What strategies would they make to maximize their profit?

As a matter of fact in this model, the choices are not made simultaneously. Obviously, no company wants to wait forever, someone has to expand the market to make profit. If the small company B expands the market first, it would have 1 million dollars deficit. Therefore, B must wait for A to expand the market first. This strategy is reasonble in real life because introducing a new product into the market always has a cost, and by the time the expansion is done by B, A gets most of the share from the market. Therefore, B must wait for A to expand the market so that B has time to prepare and take more market shares. As for A, A must know B will wait for it, but A does not want to wait either, otherwise they both get nothing. A will eventually develop and introduce the product to the market. Thus, (Expand, Wait) is a Nash Equilibruim.

Reference: https://www.youtube.com/watch?v=Upd1ESkn-Bo

Google map is the most popular mapping service in the world. Its two main features are real-time traffic conditions and route planning for traveling by foot, car, bicycle and air, or public transit. My topic is that how Google map ultilizes the graph theory to navigate users to their destinations.

In the context of CSCC46, a map can be represented as a weighted and undirected network or graph. It has nodes and edges. Similarly, Google Map can be viewed as such with nodes as locations and edges as roads. Oftentimes, people want to get to some places as fast as possible. Therefore, the Dijkstra’s algorithm comes in handy when calculating the shortest path between places. When the algorithm does is that, given a weighted graph, a starting point and an endpoint within the graph itself, the algorithm finds a path at minimum weight. In the case of Google map, it finds the fastest route from one point to the other as the pictures shown below.

Of course, each edge has different weight. Not only does the map take distances beween nodes into account, but also it considers the traffic volume of the road. As the pictures shown below, the red segments indicates that the traffic volume is high and the green ones mean the road is clear. Because sometimes, a fastest path does not mean a shortest path. By considering the traffic volume as another weight of edge, Google map calculates fastest paths as accurate as possible.

This example demonstrates that the pratice of information network plays an important role in our daily life. By studying it, we can have a deeper understanding how the individual entity interacts with others and how they are grouped together to become a network so that it can be an important reference when a new technology is being developed.

Reference: https://magazine.impactscool.com/en/speciali/google-maps-e-la-teoria-dei-grafi/