I've been wondering about the game theory of connection requests. I tend to mentally classify connection requests in terms of "people who I can help" vs. "people who can help me." I find myself eager to accept requests in the latter category, and reluctant to accept requests in the former category. I concede that this may be totally unfair. And it leaves me wondering what my optimal strategy ought to be.
So, assume you are optimizing for career success, which means you want to hire good people when you have a job, and find good jobs when you don't.
Given that, is a big network necessarily better? Are there "bad" connections? Are there "dilution" effects?
If bigger networks are better, then connection requests are just ultimatum games; someone else is asking for permission to raise your utility and theirs at the same time, and you have veto power.
But if larger networks aren't better, then what does the payoff matrix look like? Who should you try to link to? Whose connections should you ignore?