This summer, I had a wonderful opportunity to work with Professor Wayne Gao on the problem of network formation and bargaining. Networks are prevalent and significant in various social and economic scenarios, and thus many scholars have studied how the networks are formed and how surpluses are distributed among participants given a network structure. However, these two problems, although closely related, are usually studied separately.
In our project, Professor Gao proposed an umbrella framework under which these two network problems could be modeled in a consistent manner. Based on this theory, I worked on concrete examples where one or two individuals (called center individuals) could choose to connect to one or more individuals in the peripheral. In particular, I proofread and sorted out previous work, carried out numerical calculations of utilities, and wrote mathematical proofs with respect to pairwise stable networks. In addition, I was also given an opportunity to explore data management softwares, such as Mathematica, Matlab and Eclipse, and to seek online resources to build algorithms on my own.
Through this project, I learned lots of research skills such as how to keep my writing logically coherent and clear. I also mastered some management techniques for making steady progress towards our goals. For example, I found it useful to leave some routine work to do such as sorting out files every day instead of doing it all at once, since it really helps to alleviate stress and anxiety created by “being stuck at a challenging problem which I just can’t solve”. Even when all my trials of solutions to the difficult problem are fruitless, I still feel like I have achieved something.
Furthermore, this project gave me a picture of what research looks like in social sciences. As I plan to pursue a career in academia related to math, this research helped me understand how math could be beautifully used to model phenomena in our daily lives. Now I am more determined towards my goal and have a clearer vision of how to merge my capacities in mathematics and my interests in social science topics. I am really grateful for this summer opportunity and I am looking forward to continuing this project with Professor Gao in the future.
To see my poster, visit Penn Presents: https://presentations.curf.upenn.edu/poster/unified-model-network-format...