Linear complementarity models of Nash-Cournot competition in bilateral and POOLCO power markets

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Abstract
Two Cournot models of imperfect competition among electricity producers are formulated as mixed linear complementarity problems (LCPs), and a simple example is presented to illustrate their application. The two models simulate bilateral markets. The models include a congestion pricing scheme for transmission, but other transmission pricing approaches can also be represented in this framework. The two models differ from each other in that one has no arbitrage between nodes of the network, while in the other model, arbitragers erase any noncost based differences in price. The latter bilateral model turns out to be equivalent to a Cournot model of a POOLCO. The models differ from other Cournot market models in that they include both of Kirchhoff's laws via a DC approximation; can include arbitragers; possess unique solutions; and are readily solved by efficient LCP algorithms. The key assumption that permits their formulation as LCPs is that each producer naively assumes that its output will not affect transmission prices.