In the real world, behaviors of the people in the society cannot be directly controlled, instead they react to policies according to their own best interests while they interact with other individuals. In this talk, we discuss how we can utilize the power of mathematics and game theory to design policies that incentivize people to react in preferable ways. We first start with discussing the importance of game theory and related notions such as the Nash equilibrium. Then we discuss how to quantify social problems with the use of mathematical modeling. After discussing game theoretical ideas and mathematical modeling, we look at some examples where we can apply these approaches, such as controlling the carbon emission by implementing a carbon tax to slow down the climate change and deciding on the best non pharmaceutical policies (such as social distancing) to decrease the spread of an epidemic.