We consider an autonomous vehicle-target assignment problem where a group of vehicles are expected to optimally assign themselves to a set of targets. We introduce a game theoretical formulation of the problem in which the vehicles are viewed as self-interested decision makers. Thus, we seek the optimization of a global utility function through autonomous vehicles that are capable of making individually rational decisions to optimize their own utility functions. The first important aspect of the problem is to choose the utility functions of the vehicles in such a way that the objectives of the vehicles are localized to each vehicle yet aligned with a global utility function. The second important aspect of the problem is to equip the vehicles with an appropriate negotiation mechanism by which each vehicle pursues the optimization of its own utility function. We propose algorithms from multiplayer learning in games as such negotiation mechanisms. We show that convergence of negotiations to an optimal assignment is generally possible provided that the utilities of the vehicles are designed appropriately. Finally, by extensive simulations, we illustrate that vehicle negotiations can consistently lead to near optimal assignments.