In this project, we consider discrete-time linear covariance steering dynamic games where the objective of each player is chosen as the sum of control cost and the squared Wasserstein distance between the terminal distribution and their respective desired distribution. To solve this problem, we first turn it into a finite dimensional optimization problem for each player by using disturbance history feedback policy, and used iterative best response by solving the problem associated to each player iteratively by fixing the other player's policy. In the second approach, we associate the terminal Wasserstein distance with the expectation of a convex quadratic function of the state by linearizing around the terminal mean and covariance from the previous solution. This method allows us to turn the problem into an LQG game whose solution can be found by solving the associated Ricatti equation iteratively. Finally, we evaluate these approaches experimentally in terms of convergence and the final solution.