We consider models of financial markets in which all parties involved find incentives to participate. Strategies are evaluated directly by their virtual wealth. By tuning the price sensitivity and market impact, a phase diagram with several attractor behaviors resembling those of real markets emerge, reflecting the roles played by the arbitrageurs and trendsetters, and including a phase with irregular price trends and positive sums. The positive sumness of the players’ wealth provides participation incentives for them. Evolution and the bid-ask spread provide mechanisms for the gain in wealth of both the players and market makers. New players survive in the market if the evolutionary rate is sufficiently slow. We test the applicability of the model on real Hang Seng Index data over 20 years. Comparisons with other models show that our model has a superior average performance when applied to real financial data. Copyright © 2008 The American Physical Society.