By using the methods of equilibrium theory and variational inequality，we discuss closed loop supply chain network including manufacturers，retailers /recycling centers and demand markets with combination of forward and reverse flow under EPR． The interactions among various decisionmakers in the model coupled with the incorporation of environmental policies such as endoflife ( EOL) products emission taxes is analyzed． A multilayer supply chain network equilibrium model in Competitive Environments is built． We describe the competitive behavior of the various decisionmakers． We present the equilibrium conditions of every layer and the system，economic interpretations and establish the finite dimensional variational inequality formulation． Finally，three numerical examples are solved using the proposed algorithm to illustrate the validity of the model along with a discussion．