  Theoretical models of populations and swarms typically start with the
assumption that the motion of agents is governed by the local stimuli. However,
an intelligent agent, with some understanding of the laws that govern its
habitat, can anticipate the future, and make predictions to gather resources
more efficiently. Here we study a specific model of this kind, where agents aim
to maximize their consumption of a diffusing resource, by attempting to predict
the future of a resource field and the actions of other agents. Once the agents
make a prediction, they are attracted to move towards regions that have, and
will have, denser resources. We find that the further the agents attempt to see
into the future, the more their attempts at prediction fail, and the less
resources they consume. We also study the case where predictive agents compete
against non-predictive agents and find the predictors perform better than the
non-predictors only when their relative numbers are very small. We conclude
that predictivity pays off either when the predictors do not see too far into
the future or the number of predictors is small.
