3 A Example: a Model of Co-evolving Social Agents

3.2 Case Studies from the Results

Figure 4. Attendances (grey=went, black=stayed at home)

This seems to be fairly stochastic with some specialisation between agents, but is more accurately described as a version of globally coupled chaos [6].

In figure 5, I show some of the specific causation between the talk and action expressions of the ten agents during the last three weeks of each run of the simulation. This only shows the causation due the saidBy, saidByLast and wentLastWeek primitives that are not logically redundant. So it does not show any causation via attendance statistics, or the self-referential primitives (e.g. ISaidYesterday, IPredictiedLastWeek and IWentLastWeek). There is a small box for the talk and action expression of each agent (numbered upwards from barGoer-1 to barGoer-10). The numbers in the boxes are a the total number of backward causal lines connected to that box if one followed the causation backward (restricted to the last three weeks only). This is an indication of how socially embedded the agent is - a larger number indicates that there is more complex causal chain determining its action (or communication), passing through many other agents. A detailed example is analysed below.

Figure 5. Causation net for the last 3 iterations of the simulation

In order to illustrate social embedding I analyse a more detailed case study of agent's behaviour and the cause one can attribute to it. To give a flavour of how complex a detailed explanation of behaviour can get I will follow back the chain of causation for the action of barGoer-6 at week 100.

At week 100, barGoer-6's action expression was:

[OR [AND [OR [AND [AND [saidBy ['barGoer-4']] [OR [AND [NOT [wentLastWeek ['barGoer-3']]] [saidBy ['barGoer-3']]] [saidBy ['barGoer-4']]]] [NOT [wentLastWeek ['barGoer-3']]]] [saidBy ['barGoer-3']]] [NOT [wentLastWeek ['barGoer-3']]]] [wentLastWeek ['barGoer-4']]]

which simplifies to:

[OR

[AND

[OR

[saidBy ['barGoer-4']]

[saidBy ['barGoer-3']]]]

[NOT [wentLastWeek ['barGoer-3']]]]

[wentLastWeek ['barGoer-4']]]

substituting the talk expressions from bar goers 3 and 4 in week 100 gives:

[OR

[AND

[OR

[saidByLast ['barGoer-7']]

[wentLastWeek ['barGoer-7']]]]

[NOT [wentLastWeek ['barGoer-3']]]]

[wentLastWeek ['barGoer-4']]]

substituting the action expressions from bar goers 3, 4 and 7 in week 99 gives:

[OR

[AND

[OR

[saidByLast ['barGoer-7']]

[previous [OR [OR [T] [saidBy ['barGoer-2']]] [T]]]

[NOT [previous [ISaidYesterday]]]]

[previous [wentLastWeek ['barGoer-9']]]]

which simplifies to:

[OR

[NOT [previous [saidBy ['barGoer-3']]]]

[previous [wentLastWeek ['barGoer-9']]]]

substituting the talk expressions from barGoer-3 in week 99 gives:

[OR

[NOT [previous [[wentLastWeek ['barGoer-7']]]]]

[previous [wentLastWeek ['barGoer-9']]]]

substituting the action expressions from barGoers 7 an 9 in week 98 gives:

[OR [NOT [previous [previous [OR [OR [saidBy ['barGoer-10']] [OR [T] [OR [randomDecision] [saidBy ['barGoer-2']]]]] [F]]]]] [previous [previous [NOT [AND [saidBy ['barGoer-2']] [AND [AND [saidBy ['barGoer-2']] [NOT [AND [saidBy ['barGoer-6']] [wentLastWeek ['barGoer-6']]]]] [OR [AND [AND [AND [saidBy ['barGoer-2']] [OR [AND [saidBy ['barGoer-2']] [NOT [AND [saidBy ['barGoer-6']] [wentLastWeek ['barGoer-6']]]]] [saidBy ['barGoer-2']]]] [AND [saidBy ['barGoer-2']] [NOT [AND [AND [saidBy ['barGoer-2']] [AND [saidBy ['barGoer-2']] [saidBy ['barGoer-2']]]] [NOT [NOT [saidBy ['barGoer-2']]]]]]]] [AND [randomDecision] [NOT [saidBy ['barGoer-2']]]]]]]]

which simplifies to:

[previous [previous [NOT

[AND

[saidBy ['barGoer-2']]

[NOT [AND [saidBy ['barGoer-6']] [wentLastWeek ['barGoer-6']]]]]

substituting the talk expressions from barGoers 2 an 6 in week 98 gives:

[previous [previous [NOT

[AND

[greaterThan [1] [1]]

[NOT [AND [[greaterThan [maxPopulation] [maxPopulation]]] [wentLastWeek ['barGoer-6']]]]]

which finally simplifies to:

True

The above trace ignores the several important causal factors: it does not show the evolutionary processes that produce the action and talk genes for each agent at each week; it does not show the interplay of the agent's actions and communications upon events and hence the evaluation of expressions (and hence which is chosen next by agents); and in simplifying the expressions at each stage I have tacitly ignored the potential effects of the parts of the expressions that are logically redundant under this particular train of events. Even given these caveats the action of barGoer-6 at week 100 was determined by a total of 11 expressions, spread out over 6 other agents over three weeks.

On the other hand it is difficult to find models of the behaviour of barGoer-6 which does not involve the complex web of causation that occurs between the agents. It is not simplistically dependent on other particular agents (with or without a time lag) but on the other hand is not merely random. This agent epitomises, in a reasonably demonstrable way, social embeddedness.

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