In this chapter, we seek to study the interrelation between an equilibrium problem and the variational inequality problem. Under most natural assumption, the equilibrium problem is equivalent to an associated variational inequality. Hence, the existence results for equilibrium problems can be obtained from the existence results for variational inequality problems and vice versa. We study a problem of existence of Nash equilibrium in an oligopolistic market and show that it is equivalent to a variational inequality under the most natural economic assumption. We also study the relation between quasi-equilibrium problem and quasi-variational inequality. © 2018, Springer Nature Singapore Pte Ltd.