Comparison of pricing mechanisms in markets with non-convexities

We consider markets that are characterized by non-convexities or indivisibilities, due to the presence of avoidable costs and minimum supply requirements. The motivation for our work has been the area of electricity markets, which allow the submission of multi-part bids and take into account the technical characteristics of the generation units. Such market designs, when operated under marginal pricing, may lead to market outcomes where truthful bidding results in losses for some participants. To deal with this highly undesirable prospect, some approaches provide makewhole payments, or uplifts, as they are often called, whereas others modify the market-clearing prices to ensure sufficient revenues to the suppliers. In this work, we present and compare revenueadequate pricing approaches. These include the Semi-Lagrangean Relaxation and the so-called “Primal-Dual” approaches for generating efficient revenue-adequate prices. We supplement these schemes with a newly proposed scheme, which we refer to as Minimum Zero-Sum Uplift (MZU). To facilitate the comparisons, we apply these schemes on a stylized example that appears in the literature.