Directional sensor nodes deployment is indispensable to a large number of applications including Internet of Things applications. Nowadays, with the recent advances in robotic technology, directional sensor nodes mounted on mobile robots can move toward the appropriate locations. Considering the probabilistic sensing model along with the mobility and motility of directional sensor nodes, area coverage in such a network is more complicated than in a static sensor network. In this paper, we investigate the problem of self-deployment and working direction adjustment in directional sensor networks in order to maximize the covered area. Considering the tradeoff between energy consumption and coverage quality, we formulate this problem as a finite strategic game. Then, we present a distributed payoff-based learning algorithm to achieve Nash equilibrium. The simulation results demonstrate the performance of the proposed algorithm and its superiority over previous approaches in terms of increasing the area coverage.