Working Papers

Pay-as-bid Auctions with Private Information (available at SSRN)

The pay-as-bid auction is one of the most prominent mechanisms allocating divisible goods like energy. This paper analyzes equilibrium behavior in pay-as-bid auctions within a general environment where bidders are privately informed about their valuations. The key methodological innovation is to represent the auction as a continuum of asymmetric first-price auctions. I define an everywhere-optimal Bayes-Nash equilibrium, in which bid functions satisfy pointwise optimality, and characterize equilibrium strategies. With two bidders, I establish equilibrium uniqueness. The characterization enables accurate predictions of equilibrium bids even when estimated valuations contain small errors. For a class of linear marginal valuations, I derive closed-form solutions and show that pay-as-bid generates higher revenue than the VCG mechanism.

The Cost of Fairness in Electricity Markets (available at SSRN)

European policymakers argue that bidding zones with uniform prices ensure fairness in electricity markets. Since the result of such a fair spot market is often infeasible due to network constraints, a second stage is needed: the redispatch. This paper uses mechanism design theory to show that even a minimal fairness restriction on the first stage strictly increases procurement costs for asymmetric dispatches. In detail, I analyze a market-based redispatch mechanism where inc-dec gaming creates arbitrage profits for those producers that benefit the network the least. These results challenge the rationale for uniform bidding zones in asymmetric regions.

Recent talks

• VfS Annual Conference, September 2025, Cologne.

• EARIE Annual Conference, August 2025, Valencia.

• Meeting of the European Economic Association, August 2025, Bordeaux.

• European Workshop on Market Design, June 2025, Mannheim.

• Econometric Society European Winter Meeting, December 2024, Palma.

teaching

Economic Policy (TA, Bachelor, University of Mannheim), Spring 2022, 2023, 2024, 2025

Introductory Finance (TA, Bachelor, University of Mannheim), Fall 2016, 2018

Contact

linnenbrink[at]uni-mannheim.de