Emergence of heterogeneity and political organization in information exchange networks

We present a simple model of the emergence of the division of labor and the development of a system of resource subsidy from an agent-based model of directed resource production with variable degrees of trust between the agents. The model has three distinct phases corresponding to different forms of societal organization: disconnected (independent agents), homogeneous cooperative (collective state), and inhomogeneous cooperative (collective state with a leader). Our results indicate that such levels of organization arise generically as a collective effect from interacting agent dynamics and may have applications in a variety of systems including social insects and microbial communities.

Figure 1

(Color online) Schematic phase diagram for our model. The Investment axis is the degree that a large initial investment of resources is needed to see an improvement in accuracy: this corresponds to the nonlinearity $\alpha$ in the model. The benefit axis is the total difference in accuracy between random guessing and perfect knowledge, which corresponds to the variable $O$ in our model. In the lazy phase, random guessing is the optimal behavior. In the heterogeneous phase, a subset of agents dedicate their resources to thinking whereas the rest of the agents dedicate their resources to working (division of labor). In the homogeneous phase, all the agents dedicate the same nonzero amount of resources to thinking.

Figure 2

Score functions in the Isolated Phase as a function of thinking time $T$, for four values of $O$ and $\alpha$. In the Isolated Phase, each agent does not receive information from other agents.

Figure 3

Score functions in the Homogeneous Phase as a function of thinking time $T$, for different numbers of agents $N$, with $O=5$ and $\alpha =5$. In the Homogeneous Phase all agents share information and have the same parameters.

Figure 4

Phase diagram for $O=10$ in the space of the nonlinearity $\alpha$ and number of agents $N$. The phase transition from the heterogeneous phase as $N$ increases is due to the communal phase being more efficient than a selfish leader phase. The phase transition as $\alpha$ increases is due to the transition of the isolated phase to a $T=0$ phase. The dotted lines show the phase boundaries when Gaussian fluctuations with a standard deviation of 0.1 are added to the $T$ value of each agent.

Figure 5

Phase diagram for $N=50$ in the space of the nonlinearity $\alpha$ and thinking benefit $O$. The dotted lines show the phase boundaries when Gaussian fluctuations with a standard deviation of 0.1 are added to the $T$ value of each agent.

Figure 6

Optimal number of leaders as a function of total number of agents for a system with $O=5$ and two different fluctuation strengths. In this case, the fluctuations are parameterized by the resultant average accuracy $A$ of a leader with $T=1$.