We use a genetic algorithm to simulate play of a sender/receiver game of common interest in which players engage in anonymous, pairwise interactions. The order of an equilibrium is the number of player types that are communicated. There are many equilibria of each order, equilibria of the same order are Pareto-equivalent, and equilibria of different orders are Pareto-ranked by their order. We discover a dynamic process in which the population climbs an equilibrium payoff ladder, successively moving from an equilibrium of one order to an equilibrium of the next highest order, eventually converging on an equilibrium of the highest order.