We consider a finite, fixed-size population of mobile cooperators and free-riders. A cooperator is an individual who, at a cost to itself, provides benefits to any and all individuals in its vicinity, whereas a free-rider does not provide any benefits and thus pays no cost. Individuals are free to move to maximize their payoff, and our model allows for the interactions among multiple individuals at the same time. Using Gillespie's algorithm, we build an exact stochastic simulation of this continuous-time Markov process and find that decreasing the individuals' mobility or decreasing the size of the interaction neighborhood promotes the fixation of cooperators in the population.