Abstract for

"Interaction networks of agents that exploit resources"

We present a simple model for the evolution of knowledge networks between agents that exploit resources. In this context agents may, e.g., represent fishermen, people influenced by fashion, or companies; resources can be thought of as regions of the sea, fashions, the demand for products, or more generally a set of alternative strategies with different pay-offs. Generally, an individual agent's decision is not guided by a total knowledge of its surrounding world. Incorrect information and uncertainties about the other agents' behaviours complicate an optimal decision making. In our model, a resource is defined by its size and growth rate. Every timestep an agent can exploit exactly one resource. The agent's gain from a resource is a function of the resource size and decreases with the number of other agents exploiting the same resource. The agents' knowledge about their environment is represented by a directed graph with continuous strength links, given by its adjacency matrix with elements $w_{i j}\in [0,1]$. The strength of a connection between two agents $i$ and $j$ gives the probability that agent $i$ will `watch' agent $j$. Every agent will have at least a certain minimum knowledge $w_\text{min}$ of the rest of the world. The system's evolution is governed by the iteration of the following update steps: (i) agents $\{i\}$ exploit resources gaining a catch $\{ c_i\}$ (ii) all pairs of agents $i$ and $j$ compare their respective catches with probabilities given by the adjacency matrix $W$. If agent $i$ finds another agent $j$ with higher catch, it assumes $j$'s strategy, i.e. exploits the same resource as $j$ in the next timestep. Strategy adoption leads to a tightening of the connection between $i$ and $j$, i.e. $w_{i j}(t+1)= \min (1,w_{i j}(t)+q)$. (iii) loss of information with time $w_{i j}(t+1)=a w_{i j}(t)$. Depending on the parameters $w_\text{min}$ (minimum knowledge), $q$ (link strengthening after strategy adoption), $a$ (aging) and given resource growth rates we find a transition between a regime where networks are formed and a regime with close to zero connectivity. We investigate typical network structures in the first regime. From a classification of the lifetimes of network structures we discriminate between unstable and stable networks. We attempt a classification of the latter. Introducing measures of link stability we distinguish between `essential' and `non-essential' links. It turns out that stable network contain at least one of very few `core subgraphs'. Based on the latter notions of `stable networks' and `core subgraphs' we give an explanation of the dynamics, finding scale-free transition networks. The model shows how and when interaction networks emerge from strategy adaptions of agents that exploit resources and gives insight into mechanisms by which transitions from one metastable network to another one occurs. We interpret `core-subgraphs' as different modes of behaviour and elucidate the role which individual agents play in each distinct mode.