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This paper studies arbitrage-free financial markets with bid-ask spreads whose super-hedging prices are submodular. The submodular assumption on the super-hedging price, or the supermodularity usually assumed on utility functions, is the formal expression of perfect complementarity, which dates back to Fisher, Pareto, and Edgeworth, according to Samuelson (J Econ Lit 12:1255–1289, 1974). Our main contribution provides several characterizations of financial markets with frictions that are submodular as a consequence of a more general study of submodular pricing rules. First, a market is submodular if and only if its super-hedging price is a Choquet integral and if and only if its set of risk-neutral probabilities is representable as the core of a submodular non-additive probability that is uniquely defined, called risk-neutral capacity. Second, a market is representable by its risk neutral capacity if and only if it is equivalent to a market, only composed of bid-ask event securities. [ABSTRACT FROM AUTHOR]

The directed search model (Peters 52(5):1117-1127, ) is static; its dynamic extensions typically restrict strategies, often assuming price or match commitments. We lift such restrictions to study equilibrium when search can be directed over time, without constraints and at no cost. In equilibrium, trade frictions arise endogenously, and price commitments, if they do exist, are self-enforcing. In contrast to the typical model, there exists a continuum of equilibria that exhibit trade frictions. These equilibria support any price above the static price, including monopoly pricing in arbitrarily large markets. Dispersion in posted prices can naturally arise as temporary or permanent phenomenon despite the absence of preexisting heterogeneity. [ABSTRACT FROM AUTHOR]

This work introduces a set-theoretic foundation of deterministic bilateral matching processes and studies their properties. In particular, it formalizes a link between matching and informational constraints by developing a notion of anonymity that is based on the agents’ matching histories. It also explains why and how various matching processes generate different degrees of “informational isolation” in the economy. We illustrate the usefulness of our approach to modeling matching frameworks by discussing the classical turnpike model of Townsend. [ABSTRACT FROM AUTHOR]