Linear Complementarity Models of Nash-Cournot Competition in Bilateral and POOLCO Power Markets

Hobbs, Benjamin

doi:10.1109/mper.2001.4311384

Cited by 180 publications

(212 citation statements)

References 22 publications

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“…Notice that, for any GNE x * , the β given in Theorem 3.5 satisfies the sufficient condition (16). Thus, we can refine Corollary 3.3 to…”

Section: Assumption B the Shared Constraint Function G Has The Formmentioning

confidence: 86%

“…Assumption A is reasonable and is satisfied by Harker's example [13], a river basin pollution game [19,Section 5.3], electricity market models [4, Section IV.B], [16], [24,Section 5.3], [32,Section 1], and an internet switching model [6,Section 5]. By Assumption A, problem (1) is a differentiable convex programming problem.…”

Section: Problem Formulation and Assumptionsmentioning

confidence: 99%

“…For example, Robinson [25,26] discussed a two-sided game model of combat as an application of GNEP. Wei and Smeers [32] and Hobbs [16] formulated oligopolistic electricity models as GNEPs.…”

Section: Introductionmentioning

confidence: 99%

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Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints

Nabetani¹,

2009

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Abstract. We consider the generalized Nash equilibrium problem (GNEP), in which each player's strategy set may depend on the rivals' strategies through shared constraints. A practical approach to solving this problem that has received increasing attention lately entails solving a related variational inequality (VI). From the viewpoint of game theory, it is important to find as many GNEs as possible, if not all of them. We propose two types of parametrized VIs related to the GNEP, one pricedirected and the other resource-directed. We show that these parametrized VIs inherit the monotonicity properties of the original VI and, under mild constraint qualifications, their solutions yield all GNEs. We propose strategies to sample in the parameter spaces and show, through numerical experiments on benchmark examples, that the GNEs found by the parametrized VI approaches are widely distributed over the GNE set.

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“…Notice that, for any GNE x * , the β given in Theorem 3.5 satisfies the sufficient condition (16). Thus, we can refine Corollary 3.3 to…”

Section: Assumption B the Shared Constraint Function G Has The Formmentioning

confidence: 86%

Section: Problem Formulation and Assumptionsmentioning

confidence: 99%

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Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints

Nabetani¹,

2009

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“…A more useful construction of a pool is in order. It has recently been provided by Hobbs (1999). Hobbs model was formulated as a complementarity problem.…”

Section: A First Pool Modelmentioning

confidence: 99%

“…This provides the empirical basis of the subject. Extensive economic analysis of quite different level of technicality can also be found in journals such as the Journal of Regulatory Economics, Utilities Policy, Energy Economics, .... A computation oriented literature is also emerging (see the introduction of Hobbs (1999) for a recent survey). This paper belongs to this latter stream.…”

Section: Introductionmentioning

confidence: 99%

Variational Inequality Models of Restructured Electricity Systems

Daxhelet

Smeers

2001

Applied Optimization

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The restructuring of electricity systems can follow different paradigms that have different impacts. The objective of this paper is to show that Variational Inequalities Problems provide a natural tool for modeling electricity restructuring in a wide range of relevant situations. Besides being a convenient modeling tool, variational inequalities can also be used as an analytical instrument for assessing properties of different restructuring models. Last but not least, variational inequality models lend themselves to computation and hence to quantitative evaluations. Document type : Document de travail (Working Paper) Référence bibliographiqueDaxhelet, Olivier ; Smeers, Yves. Variational inequality models of restructured electricity systems.

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Hybrid Bertrand‐Cournot Models of Electricity Markets with Multiple Strategic Subnetworks and Common Knowledge Constraints

Zhang

2010

Restructured Electric Power Systems

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Most existing Nash-Cournot models of competition among electricity generators assume that firms behave purely Cournot or Bertrand with respect to transmission decisions by the independent system operator. Such models are unrealistic for markets in which interfaces connecting subnetworks are frequently saturated but the congestion pattern within individual subnetworks is less predictable. We propose two approaches for dealing with such situation. The first is a hybrid Bertrand-Cournot model of these markets in which firms are assumed to behave a la Cournot regarding inter-subnetwork transmission quantities, but a la Bertrand regarding intra-subnetwork transmission prices. A second approach is a Bertrand type model where transmission lines that are congested most of the time are designated as "common knowledge constraint" and treated as equality constraints by all market participants including the ISO and all generation firms. Under affine demand functions and quadratic costs, the market equilibrium of these models becomes mixed linear complementarity problems with bisymmetric positive semi-definite matrices. Numerical examples demonstrate that dividing the network into strategic subnetwork leads to prices higher than those predicted by the pure Bertrand model, but lower than those from the pure Cournot model. When public knowledge constraints are recognized in a Bertrand type model the resulting equilibrium does not show a uniform change in prices relative to the pure Bertrand model but we observe a shift in output from lower cost to higher cost generators, lower prices at the high cost nodes and higher prices at the low cost nodes.

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Linear Complementarity Models of Nash-Cournot Competition in Bilateral and POOLCO Power Markets

Cited by 180 publications

References 22 publications

Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints

Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints

Variational Inequality Models of Restructured Electricity Systems

Hybrid Bertrand‐Cournot Models of Electricity Markets with Multiple Strategic Subnetworks and Common Knowledge Constraints

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