The third party logistics (3PL) sector holds a crucial role in modern supply chains, streamlining the movement of goods and optimizing logistics operations. The 3PL industry's journey towards digitalization and sustainability reflects a crucial strategy to create an efficient and resilient supply chain. It is increasingly integrating Internet of Things technologies (IoT) within its operations. This latter is a cutting-edge technology widely used in the supply chain realm as it offers numerous advantages namely traceability and real-time decisionmaking capability. In view of growing concerns for the environment and the social welfare, supply chain actors are seeking to make various initiatives to shift to more sustainable practices. This paper studies the competition within an oligopolistic market of 3PL firms. Through the lens of game theory, we construct a mathematical model where a supply chain composed of n firms competes through pricing, IoT integration efforts and sustainability efforts. Results show that the IoT integration and sustainability efforts impact the pricing decisions of the firm. Moreover, this study highlights how the rivals' decisions on the IoT integration and sustainability efforts impact the firm's decision-making processes. Furthermore, a comparison of the model decision variables within a duopoly and an oligopolistic setting is conducted. This paper concludes to the significant impact of the rivals' strategies on the firm's decisions and profitability.