Hello! I'm trying to figure out how to find the best response functions and a Nash equilibrium when given a utility (profit) function that has a quadratic in the denominator.

For example: Consider the following version of a Cournot duopoly. Each firm produces ≥ 0. There is a constant production cost, . The resulting profit (utility) functions are:

1) Find the best response function for each firm.

2) Find a Nash equilibrium or show that there is none.

Thanks!