

Game-theoretic analysis of Smallest Unique Integer game - michaelochurch
http://swopec.hhs.se/hastef/abs/hastef0671.htm

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michaelochurch
What blew my mind when I played around with this in college was the fact that
it had infinite support (easy to prove) but also doubly-exponential in the
tail.

I could see the concave/convex behavior when I explored it computationally,
but I couldn't figure out the theoretical/equational basis for it. I was
working with a fixed number of players. I'm pleasantly surprised to see the
variable-player Poisson version is simpler. I definitely wish I knew more
stats, because the fixed-number version stumped me when I tried to solve it
directly. (I don't know if it's possible, except for N = 3.)

