I'm not really familar with the etiquette of stackexchange or mathoverflow, so I'm sorry if I didn't adhere to the standards. I can understand the problem with duplicate threads though and will add links on both sites. I have accepted the "trivial" answer on stats.stackexchange since I didn't expect any more input to come. Obviously, this doesn't mean that I'm not interested in a different perspective, especially if you feel that the given answer is incomplete. In fact, I would already be most grateful if I was pointed to some helpful resource on the topic. Or given the sketch of a solution.

A nice answer has been provided here: stats.stackexchange.com/questions/59450/… Since the equation is derived from an economics paper, there is of course some interpretation to the variables. $N$ is the number of firms in a market, and $\delta$ is the rate with which firms discount future profits. Loosely speaking, finding a solution $\alpha^*$ to the above equation corresponds to the existence of a Nash-equilibrium where firms collude on a supra-competitive price level, given noisy demand following $F(.)$.