Efficiency of information spreading in a population of diffusing agents

We introduce a model for information spreading among a population of N agents diffusing on a square LxL lattice, starting from an informed agent (Source). Information passing from informed to unaware agents occurs whenever the relative distance is <= 1. Numerical simulations show that the time required for the information to reach all agents scales as (N-alpha L beta), where alpha and beta are noninteger. A decay factor z takes into account the degeneration of information as it passes from one agent to another; the final average degree of information of the population I-av(z) is thus history dependent. We find that the behavior of I-av(z) is nonmonotonic with respect to N and L and displays a set of minima. Part of the results are recovered with analytical approximations.