Alternative Models of Restructured Electricity Systems, Part 1: No Market Power
Operations Research
Cournot Equilibrium in Price-Capped Two-Settlement Electricity Markets
HICSS '05 Proceedings of the Proceedings of the 38th Annual Hawaii International Conference on System Sciences (HICSS'05) - Track 2 - Volume 02
Manifolds of multi-leader Cournot equilibria
Operations Research Letters
Error bound results for generalized D-gap functions of nonsmooth variational inequality problems
Journal of Computational and Applied Mathematics
Pricing and inventory management in a system with multiple competing retailers under (r, Q) policies
Computers and Operations Research
A numerical algorithm for finding solutions of a generalized Nash equilibrium problem
Computational Optimization and Applications
Nonconvex Games with Side Constraints
SIAM Journal on Optimization
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Most previous Nash-Cournot models of competition among electricity generators have assumed smooth demand (price) functions, facilitating computation and proofs of existence and uniqueness. However, nonsmooth demand functions are an important feature of real power markets due, for example, to price caps and generator recognition of transmission constraints that limit exports. A more general model of Nash-Cournot competition on networks is proposed that accounts for these features by including (1) concave piecewise-linear demand curves and (2) joint constraints that include variables from other generating companies within the profit maximization problems for individual generators. The piecewise demand curves imply, in general, a nonmonotone multivalued variational inequality problem. Thus, for instance, imposition of a price cap can destroy the uniqueness properties found in previous models, so that distinct solutions can yield different sets of profits for market participants. The joint constraints turn the equilibrium problem into a quasi-variational inequality, which also can yield multiple solutions. The formulation poses computational challenges that can cause Lemke's algorithm to fail; a restricted formulation is proposed that can be solved by that algorithm.