🤖 AI Summary
Walrasian equilibrium lacks theoretical existence guarantees in non-convex markets, yet its observed frequency in European day-ahead electricity auctions varies markedly across countries (10%–80%). Method: We shift analytical focus from preference functions to the geometric structure of demand sets—recognizing that real-world bids are predominantly divisible (convex) with only limited indivisibilities—and develop an approximate equilibrium theory grounded in demand-set non-convexity. Our approach integrates micro-level commercial bid data analysis, Walrasian equilibrium theory, stochastic market modeling, and rigorous error-bound analysis. Contribution/Results: We prove that markets dominated by convex demand admit significantly tighter bounds on approximate equilibrium deviation. Empirically, we verify that approximately 80% of trading days in multiple European markets achieved equilibrium in 2023, aligning closely with theoretical predictions. This work provides the first structural explanation and quantifiable theoretical framework for high-frequency equilibrium emergence in non-convex markets.
📝 Abstract
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.