| Equilibrium analysis is a fundamental tool for the treatment of competition in multi-agent economic systems. In recent years, equilibrium analysis has been used extensively in the study of electric power systems and network communication systems that are modeled as non-cooperative games, wherein the renowned Nash equilibrium serves the key underlying solution concept. For the most part, the resulting Nash equilibrium problems are deterministic in nature and have not sufficiently addressed the important issue of uncertainty. In contrast, two-stage stochastic programming is a well-established approach to deal with optimal planning problems under uncertainty but is restricted to a monopolistic environment. This thesis proposes four basic two-stage models that combine stochastic programs with Nash equilibria in order to deal with certain multi-agent competition problems under uncertainty. In these models, the first stage is concerned with the determination of future investments in the form of production capacity expansion or sales dictated by forward contracts. The second stage is concerned with the optimal/equilibrium decisions of productions and sales under given realizations of the uncertainty.;Based on different agents' perspectives, we define four two-stage models as System-System, System-Nash, Nash-System and Nash-Nash. Three types of price functions are considered as well. In this thesis, we establish the proof of the existence of equilibrium of Nash-System models with linear and piecewise linear price functions. The cases with different price functions and sample size are tested. With the sample size increasing, the convergent trend is shown by computational results. We also adopted a diagonalization approach to solve Nash-Nash problems. Numerical results are presented and exhibited the convergence behavior as well. |
