Social Planning With the Replicator Dynamics

Approaches to social planning tend to assume that the behaviour of agents is at an equilibrium, yet in practice people’s behaviour gradually adapts to their experiences. In this letter, a model of social planning under the replicator dynamics is studied. This model allows for a social planner to control the learning process of agents by influencing the relative fitness of different strategies. The desiderata that such a social planner would ideally achieve – exponential stability and budget-balance – are described. Existence of a solution for any full-support distribution, as well as an analysis of its properties, are shown constructively by leveraging classical tools from geometric control theory. Though the solution is optimal in an environment without transfer costs, this may not generally hold otherwise. We formulate a relevant optimal control problem to model this setting, and determine performance guarantees based in our original solution.