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Under the continuous evolution of the opioid epidemic in the US, the recent increase in addiction as well as overdose deaths due to synthetic opioids, despite increased regulations on prescription practices, warrant a more long-term forward-looking approach incorporating the strategic responses of the other stakeholders. In this work, we model the interactions between the multiple stakeholders, as a three player non-cooperative differential game between the government, health-care providers and the illicit drug providers. The state dynamics for our differential game approach is built upon a recent data-driven epidemiological model on the opioid addiction in Tennessee, extending it to include the effects of the controls or strategies of the three players. In this paper, we compute the open loop Nash Equilibrium using the minimum principle and analyze the equilibrium control strategies of the three players and compare the optimal state trajectory of the system with that of the uncontrolled system.