Variational Inequality and Distributed Learning for a Bidding Game in Electricity Supply Markets

This study uses a game-theoretic analysis of bid-based electricity supply market equilibrium. Electricity supply markets are modeled as strategic interactions of bidders that supply electric power to the market and the bidders' pure strategies are the cost function parameters of power generation. We demonstrate that the resultant bidding game is a convex game and has a unique pure-strategy Nash equilibrium (PNE) when the bid-cost functions are parameterized by marginal costs of power generation. The PNE of the power-supply bidding game is reformulated in terms of a variational inequality and as a fixed-point of a recursive mapping. We propose two distributed learning algorithms and their variations with convergence analysis to compute a PNE. Three types of measures are proposed and analyzed for quantification of inefficiency due to falsified bidding actions corresponding to the marginal cost function parameters of supply-market participative generators. A numerical case study with a 26-bus power network is presented to illustrate and demonstrate our results.