Data injection attacks have recently emerged as a significant threat on the smart power grid. By launching data injection attacks, an adversary can manipulate the real-time locational marginal prices to obtain economic benefits. Despite the surge of existing literature on data injection, most such works assume the presence of a single attacker and assume no cost for attack or defense. In contrast, in this paper, a model for data injection attacks with multiple adversaries and a single smart grid defender is introduced. To study the defender-attackers interaction, two game models are considered. In the first, a Stackelberg game model is used in which the defender acts as a leader that can anticipate the actions of the adversaries, that act as followers, before deciding on which measurements to protect. The existence and properties of the Stackelberg equilibrium of this game are studied. To find the equilibrium, a distributed learning algorithm that operates under limited system information is proposed and shown to converge to the game solution. In the second proposed game model, it is considered that the defender cannot anticipate the actions of the adversaries. To this end, we proposed a hybrid satisfaction equilibrium - Nash equilibrium game and defined its equilibrium concept. A search algorithm is also provided to find the equilibrium of the hybrid game. Numerical results using the IEEE 30-bus system are used to illustrate and analyze the strategic interactions between the attackers and defender. Our results show that by defending a very small set of measurements, the grid operator can achieve an equilibrium through which the optimal attacks have no effect on the system. Moreover, our results show how, at equilibrium, multiple attackers can play a destructive role towards each other, by choosing to carry out attacks that cancel each other out, leaving the system unaffected.