Tuning of discretization in bimatrix game approach to power system market analysis

An important aspect of the study of power system markets involves the assessment of strategic behavior of participants maximizing their profits. In models of imperfect competition of a deregulated electricity system, the key task is to find the Nash equilibrium. In this paper, the bimatrix approach for finding Nash equilibria in electricity markets is investigated. This approach determines pure and mixed equilibria using the complementary pivot algorithm. The mixed equilibrium in the matrix approach has the equal number of nonzeros property. This property makes it difficult to reproduce a smooth continuous distribution for the mixed equilibrium. This paper proposes an algorithm for adjusting the quantization value of discretization to reconstruct a continuous distribution from a discrete one.