Since it depends on where you rank amongst the other users, you'd have to make some assumptions about how they're going to behave (and those assumptions are going to be wrong).
I think it's better to essentially use a numerical solver in this setting, rather than try to find an analytical solution.
Sounds like a great project for an econ grad student. Derive the Nash equilibria, whether numerically or analytically, grab the behavioral data from stacker.news, and test whether users are behaving according to game theoretic predictions.
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SN is like a fucking gold mine for graduate-level research. We have a new econ guy starting on Monday that I am aiming to entice...
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Well, we know users aren't, since we're all zapping different amounts, but there is a treasure trove of data for an enterprising behavioral or experimental econ PhD student.
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