We consider an economy where a finite set of agents can trade on one of two asset markets. Due to endogenous participation the differ in the liquidity they provide. Traders have idiosyncratic preferencesnfor the markets, e.g. due to differential time preferences for maturity dates of futures contracts. For a broad range of parameters we find that nontrade, trade on both markets (individualization) as well as trade on one market only (standardization) is supported by a Nash equilibrium. Byncontrast, whenever the number of traders becomes large, the evolutionary process selects a unique stochastically stable state which corresponds tonthe equilibrium with two active markets and coincides with the welfare maximizing market structure.