Fig. 1. Example configuration of K=5 targets (bars) containing a total of R=100 rewards and N=50 agents (triangles) in a d= one-dimensional world of size A_world=100. Targets are occupying 10% (a=0.1) of the world size.

Fig. 2. Reward collection times Twith varying number of targets (separate graphs for K=1,K=5,K=20,K=50) for a population of N=10,50,100 and 500 agents with a=0.1,r=2,c=1 and d=1. Each point represents the mean of 1000 trials. Points marked at σ=0 (left) represent times resulting from sole collection of agent(s) finding the target while all other agents were free to explore the world for additional targets, i.e. no information transfer occurred. Points marked at σ=100 (right) are not to be confused with the points calculated from σ=100, but instead represent times resulting from collection by all agents immediately after a target had been located by a single agent (or more than one agent simultaneously). Points marked □ represent the optimum value for σ for target location broadcasting, resulting in minimum reward collection time.

Fig. 3. Comparison of reward collection times T for a population of N=10,50,100,500 agents and K=1,5,20,50 targets (summary of previous Fig. 2 now representing points marked ,,□ there as bars). Each bar represents the mean of 1000 trials (please note the different scales for the mean time). All parameters as in Fig. 2. Three bars are shown for each combination of Nand R. The bar on the left represents the time taken to collect all rewards without communicating the location of targets to any other agent (no assistance). The bar on the right represents the time taken if all agents are collecting the rewards immediately after their discovery by at least one agent (reliable assistance). The bar in the center, which is always either lower or at least the same height as the other two bars, indicates the time taken when only the optimumnumber of agents participated in the collection of rewards while all other agents continued the search for new targets (optimum assistance). This optimum number was determined from simulation runs using σ=0,1,2,3,4,5,10,15,20,…,100 and marked with □ in previous graphs.

Fig. 4. Mean reward collection times T under optimum conditions (σ=σ_opt) for varying number of agents N and targets K (mean of 1000 trials). All parameters as in Fig. 2. The logarithmic plot shows the power law relationship between both, the number of agents and the mean minimum collection time and also the number of targets and the collection time. Under optimal conditions an increase in agents will have a positive effect on the overall collection time T. For a large number of targets this effect is dramatic but weakens with an increase in agent numbers.