Adaptive Control and the Interaction of Two Agents:

The following example illustrates some of the issues under discussion [15]:

Two agents interact in an environment which is influenced by three factors:

(i)

an unpredictable world, which accounts for all factors that are not directly accessible to modelling and control and provides a background unpredictable influence.

(ii)-(iii)

the actions of each of the two agents.

The goal of each of the two agents is to avoid crises and keep the environment predictable. Thus they have to adapt their strategies to their environment. Their success is measured by how well the future state of the environment can be predicted over some number of time steps.

The strategies that the agents have available are:

(i)

build a model of the environment with a level of complexity that the agents can choose.(The level of complexity is expressed as the number of parameters that go into the model)

(ii)

the number of observations used to tune the model.

(iii)

try to influence and control the environment to make it better predictable

(iv)

choose the type of order that the agent tries to impose onto the dynamics of the environment in order to achieve maximal predictability.

Since there are continuous unpredictable influences from the outside world and since the opponent also influences the environment in an unpredictable fashion, each agent has to continuously update the strategy. Simulations of this simple model provide some fairly interesting results: First of all both agents will try to control their environment/opponent but soon will realize that a ``leader/follower'' configuration allows better prediction for both agents.

The attempt of a leader to introduce static order in the environment appears to be generally very unstable since it provides very little information about the internal state of the system and the opponent. Therefore the model of the dominating and controlling agent becomes increasingly worse until the mismatch between model (``ideology'') and reality is large enough that the system becomes unstable and large scale fluctuations can build up. It appears that the most stable strategy of the leader is to impose a goal dynamic on the system which shows low level chaos. Thereby the controlling agent can continuously test an extended behavioral domain of the system and thereby keep the model up to date and close to reality (in the form of external world, immediate environment and opponent.) From the perspective of the follower, fairly accurate short time predictions are also possible since the goal dynamics was assumed to be weakly chaotic. That means it is unpredictable enough to keep the follower alert but also structured enough to allow for successful adaptation and anticipation. When the system becomes too unpredictable or hopeless, a transition to a ``no future'' culture might be the response.

It is very interesting to notice that the degree to which the external world is changing is essential for the degree of complexity of the most successful models for both leaders and followers: In a relatively stationary environment it pays to accumulate many data points in order to construct a model with a large number of parameters accurately. In the case of a rapidly changing world, however, sub-optimal, smaller models that need less input data and has fewer parameters to be estimated appear to become more successful, since they can be updated more rapidly, whereas a highly complex model can find itself to make accurate predictions based on data or parameters that are already obsolete. Such conditions typically occur in crisis situations where simple adaptive models with tight links to global information systems might become superior in spite of their global character and lack of detail.