Theory of Social Networks Applied to an Evolutionary Minority Game: an Agent Based Model in Swarm

While the MG is born as the mathematical formulation of “El Farol Bar” problem considered by Arthur (1994), it goes way beyond this one, since it generalizes the study of how many individuals may reach a collective solution to a problem under adaptation of each one’s expectations about the future. In Arthur (1994) the “El Farol Bar” problem was posed as an example of inductive reasoning in scenarios of bounded rationality. The olympic rationality which is usually assumed in economics – perfect, logical, deductive rationality – is extremely useful in generating solutions to theoretical problems, but it fails to account for situations in which our rationality is bounded (because agents can not cope with the complexity of the situation) or when ignorance about other agents ability and willingness to apply perfect rationally lead to subjective beliefs about the situation. Even in those situations, agents are not completely irrational: they adjust their behaviour based on what they think other agents are going to do, and these expectations are generated endogenously by information about what other agents have done in the past. On the basis of these expectations, the agent takes an action, which in turn becomes a precedent that influences the future behaviour of agents. This creates a feedback loop: expectations arise from precedents and then create the actions which, in turn, constitute the precedents for the next step.