The minority game is a generic model of competing adaptive agents, which is often believed to be a model of financial markets. We discuss to which extent this is a reasonable statement and present minimal modifications that make this model reproduce stylized facts. The resulting model shows that without speculators, prices follow random walks, and that stylized facts disappear if enough speculators take into account their market impact. (C) 2001 Elsevier Science B.V. All rights reserved.