Approximate Equilibria in Nonconvex Markets: Theory and Evidence from European Electricity Auctions

Abstract

A fundamental challenge in the design of nonconvex markets is the absence of existence guarantees for Walrasian equilibria. Despite this lack of guarantees, we observed that the European day-ahead electricity auction attained equilibrium on approximately 80% of days during 2023 in some countries, while in others, it occurred on about 10% of days. By analysing auction microdata, we attribute these differences to varying ratios of divisible (convex) bids versus indivisible (nonconvex) ones. To provide a theoretical foundation for this empirical observation, we refine classical approximate equilibrium theorems to establish a link between the market share of nonconvex participants and the existence of (approximate) equilibria. These findings offer new insights into the conditions under which equilibria can emerge in practice and contribute to current policy discussions on the reform of the European electricity auction.