Traditional asset-pricing theories assume complete market participatio
n, despite considerable empirical evidence that most investors partici
pate in a limited number of markets. We show that once the participati
on decision is endogenized, market properties change dramatically. Fir
st, limited market participation can amplify the effect of liquidity t
rading relative to full participation; under certain circumstances, an
arbitrarily small aggregate liquidity shock can cause significant pri
ce volatility. Second, there exist multiple equilibria with very diffe
rent participation regimes and levels of asset-price volatility. Third
, under plausible conditions the equilibria can be Pareto-ranked; the
Pareto-preferred equilibrium is characterized by greater participation
and lower volatility.