Scoring auctions with non-quasilinear scoring rules

In this paper we analyse scoring auctions with general non-quasilinear scoring rules. We assume that cost function of each firm is additively separable in quality and type. In sharp contrast to the recent results in the literature we show the following. (i) Equilibria in scoring auctions can be computed without any endogeneity problems and we get explicit solutions. (ii) We provide a complete characterisation of such equilibria and compare quality, price and expected scores across first-score and second-score auctions. (iii) We show that such properties and rankings depend on the curvature properties of the scoring rule and the distribution function of types.