The timber supply chain encompasses the processes involved in the sustainable extraction, processing, and distribution of timber products. This complex network involves coordination among forest owners, loggers, sawmills, wholesalers, and retailers to ensure efficient flow from forest to end consumers. Understanding the gaps and barriers in the timber supply chain is essential for promoting economic growth, environmental sustainability, and social responsibility within the forestry industry. In this paper, we employ a game theory approach to explore the interactions among forest landowners (suppliers), wood-using mills (demand for timber), and a carbon offset aggregator (demand for carbon) as market agents to provide insights about the trade-offs faced by forest landowners. We develop a timber supply chain model based on common landowner decision criteria, such as maximizing forest value,  in the US South. In this model, landowners harvest timberland to maximize their profit while taking carbon sequestration into account. Our study examines the trade-off between timber harvesting and harvest deferral for carbon sequestration based on landowners' environmental awareness. A Bertrand game has been designed to determine the Nash equilibrium pricing strategy for timber price and carbon price- based on forest structure and landowners' environmental awareness. Our findings indicate a positive association between carbon sequestration and landowners' willingness to participate in carbon programs. Our findings help to analyze the future trends in the timber market, including supply levels, demand growth, and price movements. This line of inquiry can provide valuable insights for aggregators and forest products mills on strategically planning which wood basins are more suitable for their needs. Additionally, it allows landowners to better comprehend an additional income source (carbon offsets) and complement it with more established sources of income.