The Structure of Equilibria in Trading Networks with Frictions

Abstract

Several structural results for the set of competitive equilibria in trading networks with frictions are established: The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, and a groupincentive-compatibility result hold with imperfectly transferable utility and in the presence of frictions. While our results are developed in a trading network model, they also imply analogous (and new) results for exchange economies with combinatorial demand and for two-sided matching markets with transfers.

The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects

“…21 By contrast, Kelso and Crawford (1982) imposed a gross substitutability condition at all price vectors. Imposing Kelso and Crawford's (1982) condition at every money endowment leads to a strictly stronger condition than Definition 4(a) in the presence of income effects (Schlegel, 2020).…”

Competitive Equilibria in Matching Models With Financial Constraints

“…The lattice properties of competitive equilibria and stable outcomes have been established in matching models without financial constraints, for example, Shapley and Shubik (1971), Demange and Gale (1985), Hatfield and Milgrom (2005), Ostrovsky (2008), Hatfield and Kominers (2012), Hatfield et al (2013), Kojima et al (2018), Schlegel (2021), and Candogan et al (2021). We investigate next whether QCCEs have the lattice property.…”

“…Our novel notion of QCCE remedies the nonexistence problem and recovers the equivalence with stable outcomes and core outcomes in the presence of financial constraints, together with other new structural properties of QCCEs. Fleiner et al (2019) and Schlegel (2021) analyze the existence and structural properties of competitive equilibria in models of trading networks where agents have general utility functions. Fleiner et al (2019) show the existence of competitive equilibrium and the equivalence between competitive equilibrium outcomes and trail-stable outcomes.…”

“…Fleiner et al (2019) show the existence of competitive equilibrium and the equivalence between competitive equilibrium outcomes and trail-stable outcomes. Schlegel (2021) studies the existence of competitive equilibrium with uniform prices and some other properties of competitive equilibria, for example, the lattice property, the rural hospital theorem, and incentive compatibility. Fleiner et al (2019) discuss how their general utility functions accommodate continuous market frictions like transaction taxes and soft financial constraints, but discontinuous market frictions like hard financial constraints are explicitly ruled out.…”

Equilibria in Matching Markets with Soft and Hard Liquidity Constraints

“…Notions like competitive equilibrium, stable outcome, and core outcome, and their structural properties have been intensively studied in all sorts of matching models when agents have general utility functions, see, e.g., Crawford and Knoer (1981), Quinzii (1984), Demange and Gale (1985), Legros and Newman (2007), Fleiner et al (2019), and Schlegel (2021). A matching model with general utility functions can be used to analyze matching models with soft liquidity constraints, but not to study matching models with hard liquidity constraints, which are fundamentally di¤erent.…”