We deal with three competitive location problems based on the classical Maximal Covering Location Problem. The environment of these problems consists of an open market with two non-cooperative firms (leader and follower), several customers and locations where facilities can be located. In order to capture the demand of the customers, the leader enters the market by locating a set of facilities knowing the potential locations where the follower can locate her facilities after the leader's decision. We consider here three pairs of objective functions for the leader/follower previously studied in the literature: maximizing/minimizing the demand captured by the leader, minimizing/maximizing the regret of the leader, maximizing the demand captured by each firm (also known as Stackelberg). For each model, we propose an linear integer programming formulation with a polynomial number of variables and an exponential number of constraints. The formulations are solved by branch-and-cut algorithms where the constraints are generated on demand by solving appropriated separation problems. We report extensive computational experiments realized on instances inspired by those from the literature, comparing our algorithms with the exact and heuristic algorithms previously published for these problems.