This work explores the potential of game theory to solve the task allocation problem in multi-robot missions. The problem considers a swarm with dozens of drones that only know their neighbors, as well as a mission that consists of visiting a series of locations and performing certain activities. Two algorithms have been developed and validated in simulation: one competitive and another cooperative. The first one searches the best Nash equilibrium for each conflict where multiple UAVs compete for multiple tasks. The second one establishes a voting system to translate the individual preferences into a task allocation with social welfare. The results of the simulations show both algorithms work under the limitation of communications and the partial information, but the competitive algorithm generates better allocations than the cooperative one.