Example 2 - Extending the `El Farol Bar' Model

A Case study from the results

Here I have chosen a five agent simulation at date 100. In this simulation the agents judge their internal models the utility they would have resulted in over the past five time periods. This utility function that agents get is 0.4 if they go when it is two crowded, 0.5 if they stay at home and 0.6 if they go when it is not too crowded (where too crowded means greater than 60% of the total population). This is supplemented with an extra 0.1 of utility for every one of their friends that go if they do.

The friendship structure is chosen at random (within set limits on the minimum and maximum number of friends each can have) at the beginning, and in this case is as show in figure 9.

Figure 9. Imposed friendship structure

The best (and hence active) genes of each agent are summarised above in figure 10. I have simplified each so as to indicate is logical effect only. The actual genes contain much logically redundant material which may put in an appearance in later populations due to the activity of cross-over in producing later variations.

Figure 10. Best talk and action genes at date 100

The effect of the genes is tricky to analyse even in its simplified form. For example agent-1 will tell its friends it will go to El Farol's if the average attendance over a previous number of time periods equal to the number who went last time is greater than the predicted number indicated by the trend estimated over the same number of time periods but evaluated as from the previous week! However its rule for whether it goes is simpler - it goes if it went last week.

You can see that for only one agent does what it says indicated what it does in a positive way (agent-4) and one which will do the exactly the opposite of what it says (agent-2). It may seem that agent-1 and agent-3 are both static but this is not so because figure 10 only shows the fittest genes for each agent at the moment in terms of the utility they would have gained in previous weeks. During the next week another gene may be selected as the best.

The interactions are summarised in figure 11, which shows the five agents as numbered circles. It has simple arrows to indicate a positive influence (i.e. if agent-2 says she is going this makes it more likely that agent-4 would go) and crossed arrows for negative influences (e.g. if agent-2 says she will go this makes it less likely she will go). The circles with an "R" represent a random input.

Figure 11. Talk to action causation at week 100

In the original formulation of the El Farol problem one can show that there is a game-theoretic `mixed strategy' equilibrium, where all agents should decide to go according to a random distribution weighted towards going 60% of the time - a behaviour that the deterministic model of Brian Arthur does approximate in practice, [22]. However, this model shows the clear development of different roles*1.

By the end of the run described above agent-3 and agent-1 had developed a stand-alone repetoire of strategies which largely ignored what other agent said. Agent-3 had settled on what is called a mixed strategy in game theory, namely that it would go about two-thirds of the time in a randomly determined way, while agent-1 relied on largely deterministic forecasting strategies.

The other three agents had developed what might be called social strategies. It is not obvious from the above, but agent-2 has developed its action gene so as to gradually increase the number of `NOT's. By date 100 it had accumulated 9 such `NOT's (so that it actually read NOT [NOT [... NOT [Isaid]...]]). In this way it appears that it has been able to `fool' agent-4 by sometimes lying and sometimes not. Agent-4 has come to rely (at least somewhat) on what agent-2 says and likewise agent-5 uses what agent-4 says (although both mix this with other methods including a degree of randomness).

Thus although all agents were indistinguishable at the start of the run in terms of their resources and computational structure, they evolved not only different models but also very distinct strategies and roles. They certainly do not all converge to the game-theoretic mixed-strategy mentioned above (but a few do). Thus allowing social aspects to emerge has resulted in a clear difference in the behaviour of the model.

Generated with CERN WebMaker