This paper identifies two notions of substitutes for auction and equilibrium analysis. Weak substitutes, the usual price-theory notion, guarantees monotonicity of Tatonnement processes and convergence of clock auctions to a pseudo-equilibrium, but only strong substitutes, which treats each unit...

Traditional economics focuses on hypothetical markets in which prices alone can guide efficient allocation, with no need for central organization. Such models build from Adam Smith's famous concept of the invisible hand, which guides markets and renders regulation or interference largely...

In many economic applications involving comparisons of multivariate distributions, supermodularity of an objective function is a natural property for capturing a preference for greater interdependence. One multivariate distribution dominates another according to the `supermodular stochastic...

How do discount rates affect agents’ decisions and valuations? This paper provides a general method to analyze this question, allowing stochastic and managed cash flows, stochastic discount rates, and time inconsistency and including arbitrary learning and payoff or utility processes. We show...

We present a model for the equilibrium movement of capital between asset markets that are distinguished only by the levels of capital invested in each. Investment in that market with the greatest amount of capital earns the lowest risk premium. Intermediaries optimally trade off the costs of...

Orderings of interdependence are useful in many economic contexts: in assessing ex post inequality under uncertainty; in comparing multidimensional inequality; in valuing portfolios of assets or insurance policies; and in assessing systemic risk. We explore five orderings of interdependence for...