Quarto is a great game, and I think it's well suited for an app like this where you can take your time thinking about your turn. However, it would be nice to give the game designer some credit.
I like your design, but I think you need some copy on privacy and data security. For physician access, how do you handle HIPAA compliance? It would be good to mention this on the front page, at least under the "For Physicians" section.
Your description of research as "pebbles" reminds me of this representation of PhD research (posted on HN a couple years ago). I like how it captures the idea of pushing out the boundaries of what we know just a tiny bit at a time.
This book provides a great introduction to game theory. What I like best about it is the way that it introduces simple examples in the first chapter, and then expands upon these examples in the following chapters, adding new complications each time.
One (not uncommon) scenario is when two identical (or high match) assignments are turned in, and the professor does not know if (1) the students collaborated or (2) one student cheated off of the other. Penalizing both students is clearly wrong if one student did the assignment properly without cheating, and the other student copied the first student's work.
How can the professor determine which student cheated (or if both students cheated), without spending substantially time looking into it and talking to both students?
Do you have any plans to license the software to clients, where we could use it on our own servers? The functionality looks great, but I have concerns about proprietary and confidential information.
I partially disagree. I think in a graduate program at least (esp. one that requires close relationships with faculty, like a PhD), it is reasonable to assume that most of the student are passionate about their subject. But professors have limited time, and the article is correct that the approach matters when trying to get attention from faculty. As the article argues, proving that you are not wasting their time is key for professors to decide how to allocate their time spent working with students.