Walrasian equilibria from an optimization perspective: A guide to the literature

Bichler, Martin; Fichtl, Maximilian; Schwarz, Gregor

doi:10.1002/nav.21963

Cited by 10 publications

(7 citation statements)

References 69 publications

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“…In fact, it is well known that WE only exist for restricted types of valuations for which the LP relaxation actually yields a feasible integer solution. For example, if all bidders' valuations are strong substitutes, this is a sufficient condition for WE to exist (Bikhchandani and Mamer 1997, Leme 2017, Baldwin and Klemperer 2019, Bichler et al 2020. In practice, these conditions are rarely satisfied.…”

Section: Competitive Equilibriummentioning

confidence: 99%

Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response

Bichler

Knörr

Maldonado

2023

Information Systems Research

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Climate change and the transition to renewable energy sources have had a significant impact on wholesale electricity markets. This has led to renewed interest in the design of electricity markets and pricing rules for spot markets. It is well known that theoretical ideals such as Walrasian equilibria cannot be obtained because of the nonconvex nature of the market-clearing problem. Instead, current pricing rules compute linear and anonymous price signals, yet at these prices, market participants often make a loss. Such losses are compensated by individual side payments that distort the price signal and have thus come under scrutiny by regulators. In this article, the authors examine this issue in greater detail. In markets with price-sensitive or flexible demand—which becomes increasingly important with growing levels of renewables—there can be no linear pricing rule that avoids make-whole payments under the welfare-maximizing allocation. Motivated by this observation, the authors introduce a pricing rule that minimizes make-whole payments and compare it against alternative pricing schemes. Numerical experiments indicate how the novel pricing rule can substantially reduce make-whole payments without significant impact on the overall market price. The findings provide input for the ongoing policy debate on make-whole payments in wholesale electricity markets.

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Section: Competitive Equilibriummentioning

confidence: 99%

Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response

Bichler

Knörr

Maldonado

2023

Information Systems Research

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“…In other words, the market does not require any subsidy and the outcome is stable. Several papers dis-cusses conditions for when a Walrasian equilibrium exists (Kim 1986;Bikhchandani and Mamer 1997;Baldwin and Klemperer 2019;Leme 2017;Bichler et al 2020).…”

Section: How Can Prices Be Computed In Modern Electricity Markets and Whichmentioning

confidence: 99%

Electricity Markets in a Time of Change: A Call to Arms for Business Research

Bichler

Buhl

Knörr

et al. 2022

Schmalenbach J Bus Res

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Europe’s clean energy transition is imperative to combat climate change and represents an economic opportunity to become independent of fossil fuels. As such, the energy transition has become one of the most important, but also one of the most challenging economic and societal projects today. Electricity systems of the past were characterized by price-inelastic demand and only a small number of large electricity generators. The transition towards intermittent renewable energy sources changes this very paradigm. Future electricity systems will consist of many thousands of electricity generators and consumers that actively participate in markets, offering flexibility to balance variable electricity supply in markets with a high spatial and temporal resolution. These structural changes have ample consequences for market operators, generators, industrial consumers as well as prosumers. While a large body of the literature is devoted to the energy transition in engineering and the natural sciences, it has received relatively little attention in the recent business research literature, even though many of the central challenges for a successful energy transition are at the core of business research. Therefore, we provide an up-to-date overview of key questions in electricity market design and discuss how changes in electricity markets lead to new research challenges in business research disciplines such as accounting, business & information systems engineering, finance, marketing, operations management, operations research, and risk management.

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“…There is significant literature on computing competitive equilibria with strong substitutes valuations. See, for example, [4,11,13,21,25,35,38,39,41,42]. 4 The interest in strong substitutes is due to the fact that it captures practically relevant valuations for indivisible goods, but the allocation problem can be solved in polynomial time and Walrasian competitive equilibrium prices always exist, which is not the case for general valuations [14].…”

Section: The Strong Substitutes Product-mix Auction (Sspma)mentioning

confidence: 99%

Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices

et al. 2022

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We show the strong substitutes product-mix auction bidding language provides an intuitive and geometric interpretation of strong substitutes as Minkowski differences between sets that are easy to identify. We prove that competitive equilibrium prices for agents with strong substitutes preferences can be computed by minimizing the difference between two linear programs for the positive and the negative bids with suitably relaxed resource constraints. This also leads to a new algorithm for computing competitive equilibrium prices which is competitive with standard steepest descent algorithms in extensive experiments.

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Walrasian equilibria from an optimization perspective: A guide to the literature

Cited by 10 publications

References 69 publications

Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response

Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response

Electricity Markets in a Time of Change: A Call to Arms for Business Research

Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices

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