Uniqueness of market equilibria on networks with transport costs

Krebs, Vanessa; Schmidt, Martin

doi:10.1016/j.orp.2018.05.002

Cited by 15 publications

(5 citation statements)

References 11 publications

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“…For a related long-run model without DC power flow constraints, uniqueness of market equilibria is shown in [28]. Moreover, uniqueness of the solution of a short-run model, again without DC power flow constraints is proven in [42] for the case of transport costs. However, the most related study is given in [41].…”

Section: An Equivalent Variational Inequalitymentioning

confidence: 95%

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

2021

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We consider uncertain robust electricity market equilibrium problems including transmission and generation investments. Electricity market equilibrium modeling has a long tradition but is, in most of the cases, applied in a deterministic setting in which all data of the model are known. Whereas there exist some literature on stochastic equilibrium problems, the field of robust equilibrium models is still in its infancy. We contribute to this new field of research by considering $$\Gamma $$ Γ -robust electricity market equilibrium models on lossless DC networks with transmission and generation investments. We state the nominal market equilibrium problem as a mixed complementarity problem as well as its variational inequality and welfare optimization counterparts. For the latter, we then derive a $$\Gamma $$ Γ -robust formulation and show that it is indeed the counterpart of a market equilibrium problem with robustified player problems. Finally, we present two case studies to gain insights into the general effects of robustification on electricity market models. In particular, our case studies reveal that the transmission system operator tends to act more risk-neutral in the robust setting, whereas generating firms clearly behave more risk-averse.

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Section: An Equivalent Variational Inequalitymentioning

confidence: 95%

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

2021

Self Cite

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“…In this case, the roots of the characteristic equation: Evidently, (7) proves, initial assumption 𝑝(0) = 𝑝 0 will not be sufficient for determining constants 𝑐 1 , 𝑐 2 . Therefore, additional initial statement is needed.…”

Section: The Evans Classical and Differential Modelsmentioning

confidence: 99%

“…Turn to differential Evans model as (7). Now, assume that all its parameters are hyperparameters, without any numerical In the given case, aggregate quadratic deviation will be only 3.8334, that is the best value among all mentioned models.…”

Section: Comparing the Accuracy Of Different Evans Models With Unknow...mentioning

confidence: 99%

“…In [4] the stock exchange activity and equilibrium price in the shares market are introduced. Functioning and unique features of the equilibrium price described for transportation networks with perfect competition are regarded in [7], and, under oligopoly, in [1]. Thus, the problem of finding the solution being as well unique promotes another aspect for investigating market balance models.…”

Section: Introductionmentioning

confidence: 99%

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Modifications of Evans Price Equilibrium Model

Zabolotnii

Mogilei

2023

IAPGOS

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The paper regards the classical Evans price equilibrium model in the free product market in the aspect of regarding the opportunities for expanding (modifying) the model given that is aimed at perfecting the accuracy of its mathematical formulating. As an accuracy criterion, we have chosen a summary quadratic deviation of the calculated indices from the given ones. One of the approaches of modifying the basic Evans model is suggesting there is a linear dependence between price function and time as well as its first and second derivatives. In this case, the model will be described through differential equation of second order with constant coefficients, revealing some oscillatory process. Besides, it is worth regarding a non-linear (polynomial) dependence between demand, supply and price. The paper proposes mathematical formulating for the modified Evans models that have been approbated for real indices of exchange rates fluctuations. It also proves that increase of the differential and/or polynomial order of the given model allows its essential accuracy perfection. Besides, the influence of arbitrary restricting circumstances of the model on its accuracyis regarded. Each expanded Evans model is accompanied by mathematically formulated price and time dependence.

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“…Aussel et al [8] discuss the existence of a market equilibrium in a context similar to ours. A recent paper [9] shows the uniqueness of market equilibrium in the presence of transport costs. A justification of our market model can be found for instance in [10] and [11].…”

Section: Introductionmentioning

confidence: 99%

Procurement Auctions with Losses

Heymann

Jofré

2022

Preprint

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To study first-price procurement auctions in the presence of losses, we introduce a new fixed point gradient flow algorithm to compute the Bayesian Nash Equilibrium. We use this efficient algorithm to compare optimal, first-price and VCG auctions. This allows us to numerically estimate the social cost of sub-optimality of the nodal pricing mechanism in wholesale electricity markets. We also derive a closed form expression of the optimal mechanism procurement cost when the types are uniformly distributed. Last we show how the algorithm adapts to more general grids.

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Uniqueness of market equilibria on networks with transport costs

Cited by 15 publications

References 11 publications

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

Modifications of Evans Price Equilibrium Model

Procurement Auctions with Losses

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