Title: Applications of Nash Equilibria and Lemke's Method in Electricity
Markets

Speaker: Jong-Shi Pang, Department of Mathematical Sciences, Rensselaer
Polytechnic Institute

In recent years, Nash equilibrium models have provided a
major mathematical and computational framwork for the study of market
designs and price computation in deregulated electricity markets.  Many
of these models can be formulated as linear complementarity problems,
and some as nonlinear complementarity problems.  The renowned Lemke
pivoting algorithm continues to play a central role in the numerical
solution of the linear models and the underlying homotopy approach
remains a powerful tool for treating the nonlinear models.   This talk
presents a survey of the speaker's joint research with Benjamin Hobbs at
the Johns Hopkins University over a period of half a dozen years that
deals with a variety of such models and their solution.  These models
range from some simple one-stage Nash-Cournot games to some highly
complex two-stage games with uncertainty as well as
multi-leader-follower games, whose numerical solution challenges the
state-of-the-art methodology and software.