Competitive versus collusive Nash equilibria in affine supply function competition with quadratic costs

This paper studies strategic games of supply function competition under the assumptions that (i) the sellers can choose arbitrarily increasing or decreasing affine supply functions, (ii) they have an identical quadratic cost function, and (iii) the deterministic affine demand function is strictly decreasing. Based on the description of all symmetric Nash equilibria---and the ensuing characterization of an extreme-point price function as a Moebius transformation---, I derive an `almost anything goes' result which determines the set of all market-clearing prices that can be generated by the symmetric Nash equilibria. I discuss in detail competitive Nash equilibria---which generate the minimal equilibrium price at zero profits for the sellers---and collusive Nash equilibria---which generate the monopoly price. Both extreme types of Nash equilibria uniquely exist for non-zero quadratic costs and consist of strictly decreasing supply functions.