Repeated-game models of competitive electricity markets: Formulations and algorithms

It has long been recognized that repeated interactions among strategic players can lead to tacit collusion, a form of market power abuse that can cause significant social welfare losses. The objective of this study is to establish a canonical form of (discrete-time) dynamic-game models that is well-grounded in industrial organization theory, can model transmission networks and other fringe players in electricity markets, and is computable in order to quantify market outcomes and to provide comparative statics (sensitivity analysis). The modeling and computational framework is designed to help market regulators simulate market outcomes and identify key factors that may discourage tacit collusion. The framework can also provide benchmark results to be compared with empirical studies so that more definitive conclusions can be drawn.;In this work, repeated games are modeled as optimization problems, which contain implicit functions in their constraints and are nonconvex in general. To obtain globally optimal solutions of such problems, a branch-and-bound-type algorithm is developed. Such an algorithm utilizes special properties of the repeated-game models, and are shown to outperform general purpose global optimization solvers through numerical examples. An electricity network model is further included in the repeated-game model to better study firms' collusive strategies in deregulated electricity markets. The resulting models are formulated as mathematical programs with equilibrium constraints (MPECs), and the global optimization algorithm is extended to solve the MPECs.;Numerical examples show that market outcomes (i.e., prices and social surplus) from tacit collusion lie in between the static Nash equilibrium and joint monopoly solutions, but closer to the latter when firms are not myopic. Furthermore, collusive electricity producers can strategically de-congest a transmission line and transfer the system operator's surplus into their own profits to a greater degree than in a static Nash equilibrium. Comparative statics on parameters that may affect collusion, including firms' discount factor and the number of firms, are performed through the computational approach.