In this paper, we describe a novel game-theoretic formulation of the optimal mobile agents placement problem which arises in the context of Mobile Ad-hoc Networks (MANETs). In particular, we consider two classes of multistage games: sequential and simultaneous. For such games, the definitions of the Nash equilibria and the cooperative solution are given. The described games exhibit a number of interesting features. For instance, the Nash equilibrium may turn out to be unattainable in both a simultaneous and a sequential game. In this case, the game dynamics may exhibit the behaviour similar to that of a limit cycle albeit in a discrete space. A modelling environment for the analysis of different strategies of the players was developed in MATLAB. The programme generates various game situations and determines each players move by solving respective optimisation problems. Using the developed environment, two specific game scenarios were considered in detail.