Computable Models of Dynamic Spatial Oligopoly from the Perspective of Differential Variational Inequalities

We begin this chapter with the basic definition of Nash equilibrium and formulation of static spatial and network oligopoly models as variational inequalities (VIs), which can be solved by well-known numerical methods presented in the literature. We then move on to dynamic network oligopoly models and show the differential Nash game describing competitive network oligopoly may be articulated as a differential variational inequality (DVI) involving both control and state variables. Finite-dimensional time discretization is employed to approximate the model as a mathematical program, which may be solved by the multistart global optimization scheme found in the off-the-shelf software package GAMS when used in conjunction with the commercial solver MINOS. We also present a small-scale numerical example of differential network oligopoly approached from the DVI perspective.