Investigation of Nash Equilibrium existence involving complementarity-constrained pricing models

The goal of this paper is to study Nash Equilibrium (NE) existence of some game‐theoretic pricing models. In Soon et al. , deterministic pricing models incorporating a complete demand system were proposed. As in those models, the demand function is defined via a Nonlinear Complementarity Problem (NCP), the models’ pricing constraints include complementarity conditions. When incorporated within a game, the best response problem facing each seller is a Mathematical Program with Equilibrium Constraints. A randomized version of this pricing problem will be introduced in this work and the issue of NE existence will be discussed for both the deterministic and random pricing games.