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Formulation of oligopolistic competition in AC power networks: An NLP approach
 IEEE Transactions on Power Systems, Forthcoming
, 2007
"... Abstract—In this paper, oligopolistic competition in a centralized power market is characterized by a multileader singlefollower game, and formulated as a nonlinear programming (NLP) problem. An ac network is used to represent the transmission system and is modeled using rectangular coordinates. T ..."
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Abstract—In this paper, oligopolistic competition in a centralized power market is characterized by a multileader singlefollower game, and formulated as a nonlinear programming (NLP) problem. An ac network is used to represent the transmission system and is modeled using rectangular coordinates. The follower is composed of a set of competitive suppliers, demands, and the system operator, while the leaders are the dominant suppliers. The ac approach allows one to capture the strategic behavior of suppliers regarding not only active but also reactive power. In addition, the impact of voltage and apparent power flow constraints can be analyzed. Different case studies are presented using a threenode system to highlight the features of the formulation. Results on a 14node system are also presented. Index Terms—Competition, complementarity, Cournot, mathematical problem with equilibrium constraints (MPEC), Nash equilibrium, oligopoly. I.
On the Variational Equilibrium as a Refinement of the Generalized Nash Equilibrium
"... We are concerned with a class of Nash games in which the players’ strategy sets are coupled by a shared constraint. A widely employed solution concept for such games, referred to as generalized Nash games, is the generalized Nash equilibrium (GNE). The variational equilibrium (VE) [6] is a specific ..."
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Cited by 7 (1 self)
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We are concerned with a class of Nash games in which the players’ strategy sets are coupled by a shared constraint. A widely employed solution concept for such games, referred to as generalized Nash games, is the generalized Nash equilibrium (GNE). The variational equilibrium (VE) [6] is a specific kind of GNE given by a solution of the variational inequality formed from the common constraint and the mapping of the gradients of player objectives. Our contribution is a theory that provides sufficient conditions for ensuring that the existence of a GNE implies the existence of a VE; in such an instance, the VE is said to be a refinement of the GNE. For certain games our conditions are shown to be necessary. This theory rests on a result showing that, in both the primal and the primaldual space, the GNE and the VE are equivalent upto the Brouwer degree of two suitably defined functions, whose zeros are the GNE and VE, respectively. The refinement of the GNE is of relevance to pure, applied and computational game theory. Our results unify some previously known facts pertaining to such equilibria and are utilized in showing that sharedconstraint NashCournot games arising in power markets do indeed admit a refinement.
A game–theoretic analysis of the implications of overlay network traffic on ISP peering
 COMPUTER NETWORKS
, 2008
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A Stochastic, Multipleleader Stackelberg Model: Analysis, Computation, and Application
, 2009
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Numerical Study of Affine Supply Function Equilibrium in AC NetworkConstrained Markets
"... Abstract—An affine supply function equilibrium (SFE) approach is used to discuss voltage constraints and reactive power issues in the modeling of strategic behavior. Generation companies (GenCos) can choose their bid parameters with no restrictions for both energy and spinning reserves. The strategi ..."
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Abstract—An affine supply function equilibrium (SFE) approach is used to discuss voltage constraints and reactive power issues in the modeling of strategic behavior. Generation companies (GenCos) can choose their bid parameters with no restrictions for both energy and spinning reserves. The strategic behavior of generators is formulated as a multileader singlefollower game. Each GenCo is modeled as a leader, while the central market operator running a cost minimization process is the sole follower. An ac model is considered to represent the transmission system. A threenode system is used to illustrate several cases, and study the implications of the incentives of the strategic players to exploit active and reactive power, and spinning reserves in order to maximize profits. Results for a 14node system are also presented. Index Terms—Ac system, complementarity, market power, mathematical problem with complementarity constraints,
Two stage stochastic equilibrium problems with equilibrium constraints: modeling and numerical schemes
, 2010
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Contagion and observability in security domains
 In Proceedings of the 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), 1364–1371. IEEE
"... We examine security domains where defenders choose their security levels in the face of a possible attack by an adversary who attempts to destroy as many of them as possible. Though the attacker only selects one target, and only has a certain probability of destroying it depending on that defender’s ..."
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We examine security domains where defenders choose their security levels in the face of a possible attack by an adversary who attempts to destroy as many of them as possible. Though the attacker only selects one target, and only has a certain probability of destroying it depending on that defender’s security level, a successful attack may infect other defenders. By choosing a higher security level the defenders increase their probability of survival, but incur a higher cost of security. We assume that the adversary observes the security levels chosen by the defenders before selecting whom to attack. We show that under this assumption the defenders overprotect themselves, exhausting all their surplus, so optimal policy requires taxing security, as opposed to the subsidies recommended by alternative models for contagious attacks which do not take into account the attacker’s ability to observe the defenders ’ choices. 1
Bilevel Direct Search Method for LeaderFollower Equilibrium Problems and Applications
, 2012
"... In the paper, we propose a bilevel direct search method for the distributed computation of equilibria in leaderfollower problems. This type of direct search methods is designed for characterizing the decision making process where the players ’ objective functions are not analytically available. We ..."
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In the paper, we propose a bilevel direct search method for the distributed computation of equilibria in leaderfollower problems. This type of direct search methods is designed for characterizing the decision making process where the players ’ objective functions are not analytically available. We investigate the convergence of the accumulation points yielded by the method to the stationary points of the problems. Then, we apply the method to a health insurance problem and carry out several numerical examples to illustrate how the method performs when solving leaderfollower problems. Key words: Leaderfollower equilibrium, direct search method, stationary point, health insurance 1
52(2007) APPLICATIONSOFMATHEMATICS No.6,473–494 ON MSTATIONARYPOINTSFORASTOCHASTICEQUILIBRIUM PROBLEMUNDEREQUILIBRIUMCONSTRAINTSIN ELECTRICITYSPOTMARKETMODELING*
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