Throughout this semester, you learned two theories—graph theory and game theory—and five application areas of these theories—(1) Matching markets, (2) bargaining and power in networks, (3) link analysis and web search, (4) network effects, and (5) epidemics.
The project
- This project is in an open-book format. You can refer to any material available to you. However, your primary attention should be given to the materials discussed in class, as opposed to other web resources (e.g., Wikipedia).
- Formatting guideline:
- Page limit: 6 (minimum) – 10 (maximum) pages in total. References, tables and figures do not count towards the page count.
- Use either Times New Roman (12 font size) or Ariel (11 font size); double-space; at least 1-inch margin on all sides.
- Every material you referred to must be listed in the bibliography attached to the end of your paper. Any reference style is acceptable.
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*** Beginning of the Project Requirements ***
Throughout this semester, you learned two theories—graph theory and game theory—and five application areas of these theories—(1) Matching markets, (2) bargaining and power in networks, (3) link analysis and web search, (4) network effects, and (5) epidemics.
This final project requires you to find a current real-world problem in one of the five application areas and to apply both theories (must be BOTH theories, not just one). When you apply both theories to a problem, you must use at least one lab exercise from each theory, which means that you must use at least two graphs or equations discussed in the recitations. In order to find a proper real-world problem, you can refer to the lecture notes where I gave several examples of them. Then, you can refer to the lab exercises done during Thursday recitations to find graphs or quantifications appropriate to delineate the real-world problem you chose.
In sum, you are required to demonstrate your ability to apply and synthesize what you learned in this class (theories and exercise) to your understanding of a real-world problem. In so doing, you will increase your ability to think critically about a pressing social issue not from an individual, microscopic perspective, but from a larger, macro, and systematic perspective. As a result, you will better appreciate the benefits of learning network theories
Examples of such problems are as follows. You may use the following examples, or elect to use other examples. If you choose to use other examples, you must ensure that your chosen examples can properly represent both graph and game theories and manifest in one of the five application areas. Your choice of a problem can affect the entire quality of your project. Make sure you choose a right topic. You can always consult me during my office hours.
| Graph theory | Game theory | Application area | Graphs and/or Quantifications to use | |
| 2020 US presidential election | Balanced network
OR Homophily principle |
Nearly all the games discussed in Chapter 6, including pure and mixed strategies, and/or Pareto/social optimality | Bargaining and power in networks | Homophily, balanced network examples and many games |
| Propagation of health misinformation during the pandemic | Weak ties, Social influence, or affiliation | Best response, prisoner’s dilemma (when not knowing what others will do (in terms of wearing masks, what is your best response) | Link analysis and web search, and epidemics | Prisoner’s dilemma, social influence, and/or web search |
| Growth of monopolistic Internet giants (e.g., Facebook, Amazon) | Breadth-first search, structural balance (online ratings) | Coordination game | Matching markets, network effects | Breadth-first search, structural balance, and/or market-clearing property (optimal assignments) |
Structure of your paper and a rubric
| Grade items | Descriptions | Points allocated |
| 1. Executive Summary of the project | Give a brief yet convincing overview and summary of your project. Introduce your chosen topic, rationale for choosing the topic, illustrate the specific sub-theories you will be using (e.g., say “I’ll use a coordination game, instead of a game theory), and why you believe your chosen sub theories are adequate, and how you will quantify or graph the chosen problem. Conclude this paragraph with the new insight you gained from this anaysis. | 10 |
| 2. Introduction and Justifications for your chosen topic | Introduce the real-world problem you chose. Provide background literature to show why your chosen topic is worth an investigation, not only to you personally, but to the society as a whole. Provide statistics (e.g., the number of people affected by this issue), concrete predictions (e.g., the vaccination rate will decrease if health misinformation persists), and describe the current and future impact your chosen issue can have on the society. | 20 |
| 3. Analysis of the chosen topic, using both graph and game theories | Now, illustrate the pressing issue from the theoretical perspectives using a graph theory and then a game theory. Delineate the cause, processes, and outcome of your chosen issue. Show how you disclosed underlying reasons for your chosen issue. For instance, 2020 US presidential election demonstrated how divided our society is. But it’s not specific to the US only. According to homophily principle, people tend to flock together with others who share similar values, viewpoints, and political affiliations. Discuss what caused this division, how this division increases, and what future prospect would look like, based on the homophily principle. | 15 per theory (30 points in total) |
| 4. Quantification of your chosen issue | Include small-scale graphs or equations that best demonstrate your earlier analysis (3 above). For instance, I would graph the evolutions of positive and negative relationships in a network to show how a network becomes “balanced” when it becomes polarized. I would also present a simple game (e.g., mixed strategy) to describe what one party would do not knowing what their opponent would do to increase their payoffs. | 10 per graph or an equation (20 points in total) |
| 5. Conclusion | Based on 3 and 4 above, summarize what I can learn from your analysis. What new perspective, insight have you provided to my understanding of your chosen social issue? How is your conclusion different from what is already known? How potentially could your analysis contribute to the society? Did you provide a different or a broader angle to understanding your chosen topic? Did you provide a deeper analysis of an issue? Did you find a new application area for the two theories you learned in class? | 10 |
| 6. Quality of writing | Is this paper written in the essay format? Is this paper free from grammar errors and typos? Are all the figures, charts, and photos legible and formatted properly? Are the citations and references formatted consistently throughout? Did you follow all the formatting guidelines in this instruction? | 10 |
| Your roles in this project (applicable only if you work as a team. This section will be in the appendix and will not count towards the page limit.) | What were your roles in this project? Describe your roles and contributions as specific as possible. Point the parts of this report completed by you. Describe roles (e.g., research) other than writing. Your final grade can be adjusted based on this description. Those members who did not sufficiently contribute to the project may receive lower grades than other members. If you worked alone, this portion is not applicable. | Potential grade adjustment |
| Total | 100 |
*** End of the Project Requirements ***
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