A new concept of equilibrium in secure strategies (EinSS) in non-cooperative games is presented. The EinSS coincides with the Nash Equilibrium when Nash Equilibrium exists and postulates the incentive of players to maximize their profit under the condition of security against actions of other players. The new concept is illustrated by a number of matrix game examples and compared with other closely related theoretical models. We prove the existence of equilibrium in secure strategies in two classic games that fail to have Nash equilibria. On an infinite line we obtain the solution in secure strategies of the classic Hotelling’s price game (1929) with a restricted reservation price and linear transportation costs. New type of monopolistic equilibria in secure strategies are discovered in the Tullock Contest (1967, 1980) of two players.