What is the degree of sophistication that we have to put into the agents in agents based computer simulation models? Should we provide them with a "mind"? The answer ranges from Axelrod's simplicity principle to the use of full BDI (Beliefs, Intentions, Desires) cognitive agents. To discuss the subject we introduce here four models: one with "no-mind" agents that operate in an unstructured market, the second with "minded" agents assuring some stability to an emerging unstructured market; the third with no mind agents, that show a sophisticated outcome in a structured market and, finally, the fourth with "minded" agents in a structured market. No generalized results come from this presentation, but many useful doubts. Mainly, from the "no-mind" perspective, we show that it is possible to obtain complex patterns (as bubbles in a stock market) without BDI agents, when the market structure is highly sophisticated, and consequently abl...