Pricing in Combinatorial Exchanges

• Applicant: Professor Dr. Martin Bichler
• Subject Area: Accounting and Finance
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 391769402

• Final Report Year: 2023

Final Report Abstract

Combinatorial auctions have attracted substantial academic interest. Apart from their theoretical importance for market design, they have found application for the sale of spectrum licenses, in logistics, and in industrial procurement. However, the theory focuses almost exclusively on single-sided auctions. Many electronic market places nowadays can be organized as a combinatorial exchange, featuring multiple buyers and sellers who are allowed to submit package bids. Day-ahead electricity markets are a prime example of such markets, which are a lot less well understood. We plan to study different forms of pricing on combinatorial exchanges. In a first work package, we analyzed linear and anonymous prices as they are being used on day-ahead electricity markets. We wanted to understand the efficiency losses incurred by such prices in analytical models and numerical experiments. In a second work package, we studied non-linear and personalized prices, when they are a competitive equilibrium, and when outcomes are in the core. The core is a central solution concept in coalitional game theory, describing a stable solution for such markets. Unfortunately, such a core solution does not always exist in combinatorial exchanges. We studied when the core of the auction is empty in numerical experiments and characterized value functions, when this is the case. In addition, we considered budget constraints of buyers. Such constraints are important in the field, but they can lead to significant computational complexity as the allocation problem is not independent from the pricing problem anymore. We studied the complexity of allocation and pricing problems with budget constraints and proposed algorithms to compute prices in such markets.

Publications

• A Matter of Equality: Linear Pricing in Combinatorial Exchanges. Information Systems Research, 29(4), 1024-1043.
  Bichler, Martin; Fux, Vladimir & Goeree, Jacob
  
• Synergistic valuations and efficiency in spectrum auctions. Telecommunications Policy, 42(1), 91-105.
  Goetzendorff, Andor; Bichler, Martin & Goeree, Jacob K.
  
• Truthfulness in advertising? Approximation mechanisms for knapsack bidders. European Journal of Operational Research, 270(2), 775-783.
  Bichler, Martin & Merting, Sören
  
• Are Truthful Bidders Paying too Much? Efficiency and Revenue in Display Ad Auctions. ACM Transactions on Management Information Systems, 10(2), 1-18.
  Sutterer, Paul; Waldherr, Stefan & Bichler, Martin
  
• First‐Price Split‐Award Auctions in Procurement Markets with Economies of Scale: An Experimental Study. Production and Operations Management, 28(3), 721-739.
  Kokott, Gian‐Marco; Bichler, Martin & Paulsen, Per
  
• Strategyproof auction mechanisms for network procurement. OR Spectrum, 42(4), 965-994.
  Bichler, Martin; Hao, Zhen; Littmann, Richard & Waldherr, Stefan
  
• Walrasian equilibria from an optimization perspective: A guide to the literature. Naval Research Logistics (NRL), 68(4), 496-513.
  Bichler, Martin; Fichtl, Maximilian & Schwarz, Gregor
  
• The beauty of Dutch: Bidding behavior in combinatorial first-price procurement auctions. European Journal of Operational Research, 291(2), 711-721.
  Paulsen, Per; Bichler, Martin & Kokott, Gian-Marco
  
• Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices. Mathematical Programming, 203(1-2), 611-643.
  Baldwin, Elizabeth; Bichler, Martin; Fichtl, Maximilian & Klemperer, Paul
  
• Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response. Information Systems Research, 34(2), 652-675.
  Bichler, Martin; Knörr, Johannes & Maldonado, Felipe