Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly

In this note we investigate stochastic Nash equilibrium problems by means of monotone variational inequalities in probabilistic Lebesgue spaces. We apply our approach to a class of oligopolistic market equilibrium problems where the data are known through their probability distributions.Comment: 19 pages, 2 table

Strategic Action in the Liberalised German Electricity Market

Nowadays, a process can be observed in Germany where electricity producing and trading firms react to the electricity market liberalisation by merging market shares, since the year 2000, which reduces the number of suppliers and influences production and consumer prices. This paper discusses whether the liberalisation process will have positive or negative impacts on the environmental situation and whether this process together with a phase out of nuclear power can guarantee the intended improvement of environmental conditions without governmental regulation in Germany. This is done by modelling different strategic options of energy suppliers and their impacts on the economic and environmental situation in the liberalised German electricity market by a computational game theoretic model. Calculations with this model show that when German firms act strategically (e.g. a change in action of one firm affects the electricity price and, hence, the payoffs of other firms), the environment is better off at the cost of higher electricity prices. This result is robust to perturbations as shows by performing a sensitivity analysis.Electricity market liberalisation, game theoretic model, environmental effectiveness

Computing Cournot-Nash equilibria / 1441

Includes bibliographical references (p. 22-23)

Exploring the Role of Demand Shifting in Oligopolistic Electricity Markets

Previous work has demonstrated that the price elasticity of the demand side reduces electricity producers’ ability to exercise market power. However, price elasticity cannot capture alone consumers’ flexibility, as the latter mainly involves shifting of loads’ operation in time. This paper provides for the first time qualitative and quantitative analysis of the value of demand shifting in mitigating market power by the generation side. An equilibrium programming model of the oligopolistic market setting is developed, taking into account the inter-temporal characteristics of demand shifting. The decision making process of each strategic producer is modelled through a bi-level optimization problem, which is solved after transforming it to a Mathematical Program with Equilibrium Constraints (MPEC). The market equilibria resulting from the interaction of multiple independent producers are determined by employing an iterative diagonalization method. Case studies on a test market with day-ahead horizon and hourly resolution quantitatively demonstrate the benefits of demand shifting in limiting generation market power, by employing relevant indexes from the literature

Investigating the ability of demand shifting to mitigate electricity producers’ market power

Previous work on the role of the demand side in imperfect electricity markets has demonstrated that its self-price elasticity reduces electricity producers' ability to exercise market power. However, the concept of self-price elasticity cannot accurately capture consumers' flexibility, as the latter mainly involves shifting of loads' operation in time. This paper provides for the first time theoretical and quantitative analysis of the beneficial impact of demand shifting (DS) in mitigating market power by the generation side. Quantitative analysis is supported by a multiperiod equilibrium programming model of the imperfect electricity market, accounting for the time-coupling operational constraints of DS as well as network constraints. The decision making process of each strategic producer is modeled through a bi-level optimization problem, which is solved after converting it to a Mathematical Program with Equilibrium Constraints (MPEC) and linearizing the latter through suitable techniques. The oligopolistic market equilibria resulting from the interaction of multiple independent producers are determined by employing an iterative diagonalization method. Case studies on a test market reflecting the general generation and demand characteristics of the GB system quantitatively demonstrate the benefits of DS in mitigating producers' market power, by employing relevant indexes from the literature

Public evaluation of large projects : variational inequialities, bilevel programming and complementarity. A survey

Large projects evaluation rises well known difficulties because -by definition- they modify the current price system; their public evaluation presents additional difficulties because they modify too existing shadow prices without the project. This paper analyzes -first- the basic methodologies applied until late 80s., based on the integration of projects in optimization models or, alternatively, based on iterative procedures with information exchange between two organizational levels. New methodologies applied afterwards are based on variational inequalities, bilevel programming and linear or nonlinear complementarity. Their foundations and different applications related with project evaluation are explored. As a matter of fact, these new tools are closely related among them and can treat more complex cases involving -for example- the reaction of agents to policies or the existence of multiple agents in an environment characterized by common functions representing demands or constraints on polluting emissions

A bi-level programming approach for the shipper-carrier network problem

The Stackelberg game betweenshippers and carriers in an intermodal network is formulated as a bi-levelprogram. In this network, shippers make production, consumption, androuting decisions while carriers make pricing and routing decisions.The oligopolistic carrier pricing and routing problem, which comprisesthe upper level of the bi-level program, is formulated either as a nonlinearconstrained optimization problem or as a variational inequality problem,depending on whether the oligopolistic carriers choose to collude orcompete with each other in their pricing decision. The shippers\u27 decisionbehavior is defined by the spatial price equilibrium principle. Forthe spatial price equilibrium problem, which is the lower level of thebi-level program, a variational inequality formulation is used to accountfor the asymmetric interactions between flows of different commoditytypes. A sensitivity analysis-based heuristic algorithm is proposedto solve the program. An example application of the bi-level programmingapproach analyzes the behavior of two marine terminal operators. Theterminal operators are considered to be under the same Port Authority.The bi-level programming approach is then used to evaluate the PortAuthority\u27s alternative investment strategies