This paper studies the problem of forming and updating the network topology in a multirobot system that is simultaneously engaged in a given task. The contribution of this paper is to propose a decentralized model of how the network may evolve based on network-related payoff functions and pairwise games. As such, pairwise games provide a practical and general scheme for contacting other robots and revising the network topology. A network is deemed acceptable by all the robots using pairwise stability and pairwise Nash equilibrium. As an application, we consider networks that are generated with mutual link-based payoff functions and show that - under some assumptions regarding changes in the configuration states - each game is ensured of converging to a pairwise stable network. This approach is then integrated with a common robotic task where the network is critical to successful task completion. The resulting performance is evaluated with respect to a variety of measures including task completion, network density, and the average payoff along with comparative results with all-to-all communication.