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

The existence of Walrasian equilibrium is usually not guaranteed when some market participants have nonconvex preferences. This limitation applies to many real-world markets, including day-ahead electricity auctions. Despite this, we observed equilibrium on about 80% of days in several European electricity markets during 2023. Our analysis of commercial microdata suggests that this high frequency of equilibrium is caused by a market primarily composed of divisible (convex) bids compared to indivisible (nonconvex) ones. To explain why predominantly convex markets are more likely to reach equilibrium, we revisit classical results on approximate equilibria. Focusing on the nonconvexity of agents' demand sets rather than their preferences allows us to refine deviation bounds. This shows that better equilibrium approximations are guaranteed than previously thought. Ultimately, we apply these refined bounds to simple random markets with both convex and nonconvex agents to explain our empirical findings.