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 presents an equilibrium analysis of pay-as-bid auctions in a general environment where bidders are privately informed about their valuations. With two bidders, the auction can be represented as a continuum of asymmetric first-price auctions. I define an everywhere-optimal Bayes-Nash equilibrium with bid functions following from pointwise optimality, characterize equilibrium strategies and show uniqueness. The equilibrium characterization can be extended to the case with more than two players. Pointwise optimality in the everywhere-optimal equilibrium implies that bid flattening is less relevant than concluded by literature on strategic ironing. For a class of linear marginal valuations, I provide closed-form solutions and find that pay-as-bid creates higher revenue than the VCG mechanism.

Optimality of One-stage Mechanisms in Asymmetric Electricity Networks

Electricity markets often manage network congestion with two-stage mechanisms. First, the spot market treats all players symmetrically, regardless of their location in the asymmetric network. Second, the redispatch achieves a feasible dispatch. I use mechanism design theory to show that, under an asymmetry condition on the dispatch function, one-stage mechanisms can achieve the same dispatch with strictly lower procurement costs. In detail, I analyze the procurement costs of 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.

Upcoming Talks

• VfS Annual Conference, September 2025, Cologne.

Recent talks

• 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