Efficiency and stability in a model of wireless communication networks

We introduce a model of (wireless communication) networks: a group of agents want to communicate with each other; an agent has his own position, chooses his costly communication range, and benefits from direct and indirect communications with other agents; any two agents can directly communicate if each agent is located within another agent's communication range; they can indirectly communicate if each agent is connected to another agent through a sequence of direct communications. Although efficiency and stability are not compatible in a general context, we identify interesting subclasses of problems where an efficient and stable network exists: the uniform interval model, the uniform circle model, and the communication favorable domain. We also investigate the consequence of allowing agents to relocate their positions. For certain networks, relocation-proofness is equivalent to stability.