• A two-level CLSC network under the carbon cap-and-trade scheme. • A game-theoretic model that considers compliance and noncompliance behaviors. • Equilibrium conditions for demand markets, products prices, and carbon market. • Managerial insights and policy implications derived by extensive numerical analysis. In a cap-and-trade scheme, firms with low carbon emissions can trade their excess emission credits with other firms who generate more emissions than their allocated allowance. However, some firms do not fully comply with the imposed carbon policy and even exceed their overall emission capacity, including their dedicated credits as well as the credits purchased in the carbon market. The noncompliance behavior of these firms is often penalised by monetary fines. We are interested in a quantitative study to understand the characteristics of this noncompliance penalty. We present game theoretic models to investigate the network impact of compliance and noncompliance behavior of the players in a closed-loop supply chain operating under a carbon cap-and-trade scheme. The network equilibrium models are utilized to study the interactive behavior of the supply chain players. Extensive numerical analysis is completed to examine the effect of noncompliance penalties, remanufacturing ratios, and production emissions on the equilibrium results. The analysis arrives at important managerial and regulatory insights.