Multiple attacker data injection attack construction in electricity grids with minimum- mean-square-error (MMSE) state estimation is studied for centralized and decentralized scenarios. A performance analysis of the trade-off between the maximum distortion that an attack can introduce and the probability of the attack being detected by the network operator is considered. Within this setting, optimal centralized attack construction strategies are studied. The decentralized case is examined in a game-theoretic setting. A novel utility function is proposed to model this trade-off and it is shown that the resulting game is a potential game. The existence and cardinality of the corresponding set of Nash Equilibria (NE) in the game is analyzed. For the particular case of two attackers, numerical results based on IEEE test systems are presented. These results suggest that attackers perform better when they seize control of power flow measurements instead of power injection measurements.