Collective decisions in a search and exploration problem: comparison between the micro and the macro dynamics.

<p>The state space of the system is presented as a ternary plot characterised by Ψ_<i>U</i> + Ψ_<i>A</i> + Ψ_<i>B</i> = 1, so that vertices correspond to fully-uncommitted or fully-committed populations. Macroscopic dynamics are indicated by trajectories and equilibrium points from the ODE model of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140950#pone.0140950.e005" target="_blank">Eq (1)</a>, parametrised according to the specific configuration. The bold yellow trajectory indicates the behaviour starting from a fully-uncommitted population (Ψ_<i>U</i> = 1). Stable equilibrium points are indicated as blue empty circles, while unstable points are indicated as green empty diamonds. The density map in the background represents the results of homogeneous multiagent simulations (1000 runs). The inset shows the success rate <math><mi>S</mi></math> for macroscopic Gillespie simulations (white bars) and multiagent simulations (homogeneous in light gray and heterogeneous in dark grey). (<i>A</i>) Micro-macro link for a decision problem in which the best option is also the farthest one (<i>v</i>_<i>A</i> = 0.7 < <i>v</i>_<i>B</i> = 1 and <i>d</i>_<i>A</i> = 1.5 m < <i>d</i>_<i>B</i> = 2.5 m). The magnify-glass effect allows to appreciate the close correspondence between the stable point predicted by the macroscopic model and the results from the multiagent simulations. (<i>B</i>) Micro-macro link for a completely symmetric decision problem (<i>v</i>_<i>A</i> = <i>v</i>_<i>B</i> = 1 and <i>d</i>_<i>A</i> = <i>d</i>_<i>B</i> = 2.5 m).