Abstract This paper explains that anticipated market liquidity is an important concern for arbitrageurs considering entry into a market, a concern that can generate self-fulfilling asset prices. In the model, fixed investment costs turn a market illiquid and generate an arbitrage opportunity. The worst-case return on pledged collateral constrains arbitrageurs’ leverage. The interaction between this return and arbitrageurs’ capital makes entry decisions complementary and can create multiple equilibria. When arbitrageurs enter with capital, the market becomes more liquid; the worst-case return rises; and more arbitrageurs enter with capital. When arbitrageurs withhold capital, the market stays illiquid; the worst-case return falls; and other arbitrageurs stay out. (JEL D84, G11, G12) Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

A monotone function interval is the set of monotone functions that lie pointwise between two fixed, -monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings. First, we leverage the main result to characterize the set of distributions of posterior quantiles that can be induced by a signal, with applications to political economy, Bayesian persuasion, and the psychology of judgment. Second, we combine our characterization with properties of convex optimization problems to unify and generalize seminal results in the literature on security design under adverse selection and moral hazard. (JEL C61, C65, D72, D82, D91, G12)