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 L×L 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^-αL^β, where α and β 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 Iₐᵥ(z) is thus history dependent. We find that the behavior of Iₐᵥ(z) is nonmonotonic with respect to N and L and displays a set of minima. Part of the results are recovered with analytical approximations.