phrase-requestssingle-word-requests
They agreed to stay connected for hours in their provisional support group, looking for answers in their counterparts.
I want to change the bold part to say that they all shared the same problem.
Might end up using one of the above, but I feel like I need some more options to weigh in.
Edit for context: they all share the same rare cognitive impairment
There is the term choking in psychology. It is performing worse under pressure or if you are expected to perform well. It is also mentioned that, if you are being watched when you are performing a task, it means that performing well in this task is important. Thus, people perform worse.
The term choking is usually used in sports but you can choke in social interactions or anywhere.
Below is an explanation of choking and an example from the book "The Curse of the Self : Self-Awareness, Egotism, and the Quality of Human Life" By Mark R. Leary Professor of Psychology Duke University (2004).
Social loafing is a related term also. It is not exactly about being watched but you perform less when you are in a group or if there are people around.
In the social psychology of groups, social loafing is the phenomenon of people exerting less effort to achieve a goal when they work in a group than when they work alone.
Based on your premise, the word I believe you're looking for is "opportunity".
Opportunity: lucky chance; favorable circumstances. Dictionary.com: Opportunity
However, for most writing involving games of chance, it is usually referred to as risk vs reward. Where reward is the opposite of risk.
Best Answer
There's the straightforward co-sufferer: "one who suffers with another." (Free Dictionary)