| Name: | Edward Xiong |
|---|---|
| Email: | eyxiong@mit.edu |
| Home Institution: | Massachusetts Institute of Technology |
| Project: | Truth Learning in a Social Network |
| Mentor: | Jie Gao |
| Collaborators: | William Guo |
TODO
I met with William and Professor Gao to discuss research ideas that we could explore. William and I agreed to work on sequential learning specifically, and I read some of the more important papers on the topic. William is focusing on analyzing how adversaries can impact asymptotic learning, and I'm working on further characterizing configurations which give asymptotic learning. I have been working specifically on networks described by directed acyclic graphs, or equivalently, graphs with a fixed order of signals.
Specifically, I spent some time considering how different equilibrium strategies may affect social learning. If every agent is fully rational, they can choose any strategy in the case of a tie between the two possible values of the truth; we can characterize some such strategies with a probability $p \in [0,1]$, where each agent goes with their own private signal with probability $p$. It is straightforward to construct a family of graphs which achieves asymptotic learning for any $p > 0$, but fails for $p = 0$. I believe that, given a family $\mathcal{F}$ of graphs which achieves learning for some $p \in (0, 1]$, it also achieves learning for any other value of $p \in (0, 1]$.
I also thought about how the strength of the private signals can affect learning. After reviewing the known classes of graphs which have asymptotic learning, I saw that none of these classes depended on the value of $q$, the probability that any private signal is correct. That is, all the constructed classes achieved learning for all $q > \frac[1}{2}$. Thus I conjectured that asymptotic learning is also a property independent of $q$. I spent some time working on this problem, but I was unable to make much progress.