In this work, a modeling and algorithm based on multiagent reinforcement learning is developed for the problem of elevator group dispatch. The main advantage is that, along with the function approximation, this multi-agent solution leads to reduction of the state space, allowing complex states to be addressed with a synthesizing evaluation function. Each elevator is considered an agent that have to decide about two actions: answer or ignore the new call. With some iterations, the agents learn the weights of an evaluation function which approximate the state-action value function. The performance of solution (average waiting time - AWT), shown varying the traffic pattern, flow of people, number of elevators and number of floors, is comparable to other current proposals reported in the literature.