Mobility helps problem-solving systems to avoid groupthink

Groupthink occurs when everyone in a group starts thinking alike, as when people put unlimited faith in a leader. Avoiding this phenomenon is a ubiquitous challenge to problem-solving enterprises and typical countermeasures involve the mobility of group members. Here we use an agent-based model of imitative learning to study the influence of the mobility of the agents on the time they require to find the global maxima of NK-fitness landscapes. The agents cooperate by exchanging information on their fitness and use this information to copy the fittest agent in their influence neighborhoods, which are determined by face-to-face interaction networks. The influence neighborhoods are variable since the agents perform random walks in a two-dimensional space. We find that mobility is slightly harmful for solving easy problems, i.e., problems that do not exhibit suboptimal solutions or local maxima. For difficult problems, however, mobility can prevent the imitative search being trapped in suboptimal solutions and guarantees a better performance than the independent search for any system size.

Figure 1

Snapshot of a system of $M=100$ agents and density $\rho =0.0512$. Agents within a distance $d=\alpha d_0$, where $d_0=1/\sqrt{\rho }$ and $\alpha =1$, are connected by a link. The dashed circle of radius $d$ centered at the target agent determines its influence neighborhood, which comprises four agents in this example. Links that cross the square box borders are not shown for sake of clarity.

Figure 2

Mean computational cost $\langle C\rangle$ as function of the system size $M$ for the position-fixed scenario ($\delta =0$). The imitation probability is $p=0.5$ and the radius of the influence neighborhood is $d=\alpha d_0$ with $\alpha =0.25\left(⧫\right),1\left(\blacksquare \right),2\left(▾\right),5\left(▴\right),$ and $10(•)$. The solid curve is the result for the fully connected system and the dashed curve is the analytical result for the independent search [7]. The upper panel shows the results for the smooth landscape ($K=0$) and the lower panel for the rugged landscape ($K=4$).

Figure 3

Average connectivity $\langle k\rangle$ of the influence network as function of the system size $M$ for the position-fixed scenario ($\delta =0$). The radius of the influence neighborhood is $d=\alpha d_0$ with $\alpha =0.25\left(⧫\right),1\left(\blacksquare \right),2\left(▾\right),5\left(▴\right),$ and $10(•)$. The solid curve is the result for the fully connected network, $\langle k\rangle =M-1$. For $M\to \infty$ we have $\langle k\rangle \to \pi {\alpha }^2$.

Figure 4

Mean computational cost $\langle C\rangle$ as function of the system size $M$ for mobile agents with step sizes $\delta =0(•),0.5\left(▴\right),1\left(▾\right),$ and $100\left(\blacksquare \right)$. The imitation probability is $p=0.5$ and the radius of the influence neighborhood is $d=\alpha d_0$ with $\alpha =2$. The solid curve is the result for the fully connected system and the dashed curve is the analytical result for the independent search [7]. The upper panel shows the results for the smooth landscape ($K=0$) and the lower panel for the rugged landscape ($K=4$).

Figure 5

Mean computational cost $\langle C\rangle$ as function of the system size $M$ for mobile agents with step size $\delta =5$. The imitation probability is $p=0.5$ and the radius of the influence neighborhood is $d=\alpha d_0$ with $\alpha =0.25\left(⧫\right),1\left(\blacksquare \right),2\left(▾\right),5\left(▴\right),$ and $10(•)$. The solid curve is the result for the fully connected system and the dashed curve is the analytical result for the independent search [7]. The parameters of the rugged landscape are $N=12$ and $K=4$.

Figure 6

Mean computational cost $\langle C\rangle$ as function of the step size $\delta$ for a system of size $M=53$. The imitation probability is $p=0.5$ and the radius of the influence neighborhood is $d=\alpha d_0$ with $\alpha =1.5\left(\blacksquare \right),1.8\left(▾\right),1.9\left(▴\right),$ and $2(•)$. The horizontal dashed line is the result for the independent search $\langle C\rangle \approx 1.12$. The parameters of the rugged landscape are $N=12$ and $K=4$.

Figure 7

Time evolution of the mean pairwise Hamming distance $\overline{H}$ for single runs of a system of size $M=53$ and step sizes $\delta =0$, $\delta =10,$ and $\delta =100$ as indicated. The time $t$ is scaled by the halting time $t^{*}$ of each search. The imitation probability is $p=0.5$ and the radius of the influence neighborhood is $d=\alpha d_0$ with $\alpha =2$ (upper panel) and $\alpha =4$ (lower panel). The parameters of the rugged landscape are $N=12$ and $K=4$.