Gossip, Sexual Recombination and the El Farol Bar: modelling the emergence of heterogeneity - Bruce Edmonds

1. Introduction - the El Farol Bar

In 1994, Brian Arthur introduced the `El Farol Bar' problem as a paradigm of complex economic systems. In this model a population of agents have to decide whether to go to the bar each thursday night. All agents like to go to the bar unless it is too crowded (i.e. when more that 60% of the agents go). So in order to epitomise its own utility each agent has to try and predict what everybody else will do. The problem is set up so that any model of the problem that is shared by most of the agents is self-defeating. For if most agents predict that the bar will not be too crowded then they will all go and it will be too crowded, and vice versa.

Brian Arthur modelled this by randomly giving each agent a fixed menu of potentially suitable models to predict the number who will go given past data (e.g. the same as two weeks ago, the average of the last 3 week, or 90 minus the number who went last time). Each week each agent evaluates these models against the past data and chooses the one that was the best predictor on this data and then uses this to predict the number who will go this time. It will go if this prediction is less than 60 and not if it is more than 60.

As a result the number who go to the bar oscillates in an apparently random manner around the critical 60% mark, but this is not due to any single pattern of behaviour - different groups of agents swap their preferred model of the process all the time. Although each agent is applying a different model at any one time chosen from a different menu of models, with varying degrees of success, when viewed globally they seem pretty indistinguishable, in that they all regularly swap their preferred model and join with different sets of other agents in going or not. None takes up any particular strategy for any length of time or adopts any identifiably characteristic role. Viewed globally they seem to be acting stochastically and homogeneously, despite the fact that the whole system is completely deterministic and each agent is initialised with a different repetoire of models [12].

The purpose of this paper is to report on the difference in their behaviour when these agents are given a suitably powerful learning and communicative mechanisms and the whole system is allowed to co-evolve. It can thus be seen as an extension of the work in [2]

The approach taken is to endow each agent with a form of bounded rationality in the form of an evolutionary process among a population of competing mental models inside each agent. This is described in section 2. Then in section 3 I describe how this is applied to the El Farol Bar problem in a way which will allow social relations to emerge among the agents.

The results are considered in section 4 at the macroscopic level as well as in detail in the form of a case study of the interactions in the model at the last date of a particular (but representative) run. The heterogeneity which emerges in the discussed in section 5

Gossip, Sexual Recombination and the El Farol Bar: modelling the emergence of heterogeneity - Bruce Edmonds - 17 DEC 97

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