Chapter 5 Hybrid Bertrand-Cournot Models of Electricity Markets with Multiple Strategic Subnetworks and Common Knowledge Constraints

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.