Trading Networks with Frictions

Abstract

We show how frictions and continuous transfers jointly affect equilibria in a model of matching in trading networks. Our model incorporates distortionary frictions such as transaction taxes and commissions. When contracts are fully substitutable for firms, competitive equilibria exist and coincide with outcomes that satisfy a cooperative solution concept called trail stability. However, competitive equilibria are generally neither stable nor Pareto‐efficient.

An Invitation to Market Design

“…To adapt the deferred acceptance algorithm for broader applications, economists have explored ways of incorporating affirmative action and other priority constraints 12 and specifying contract terms beyond who matches with whom. 13 More recent work has shown that generalisations of the deferred acceptance algorithm can also be used to clear networked markets (Ostrovsky, 2008;Westkamp, 2010;Hatfield and Kominers, 2012;Hatfield et al, 2013;Fleiner et al, 2017;Morstyn et al, 2017).…”

Full substitutability

“…Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, exchange economies with indivisible goods, and trading networks (Kelso and Crawford 1982, Roth 1984, Bikhchandani and Mamer 1997, Gul and Stacchetti 1999, , Milgrom 2000, Ausubel and Milgrom 2005, Hatfield and Milgrom 2005, Sun and Yang 2006, , Ostrovsky 2008, Hatfield et al 2013, Fleiner et al 2017). Substitutability arises in a number of important applications, including matching with distributional constraints (Abdulkadiroğlu and Sönmez 2003, Hafalir et al 2013, Ehlers et al 2014, Echenique and Yenmez 2015), supply chains (Ostrovsky 2008), markets with horizontal subcontracting (Hatfield et al 2013), “swap” deals in exchange markets (Milgrom 2009), and combinatorial auctions for bank securities (Klemperer 2010, Baldwin and Klemperer 2019).…”

“…Ostrovsky () generalized the choice‐theoretic substitutability conditions to the context of supply chain networks by introducing a pair of related assumptions, same‐side substitutability and cross‐side complementarity, which impose two constraints: First, when an agent's opportunity set on one side of the market expands, that agent does not choose any options previously rejected from that side of the market; second, when an agent's opportunity set on one side of the market expands, that agent does not reject any options previously chosen from the other side of the market. Ostrovsky () and Hatfield and Kominers () showed that under same‐side substitutability and cross‐side complementarity, a stable outcome always exists if the contractual set has a supply chain structure (see also Fleiner et al 2017).…”

Lone wolves in competitive equilibria

“…Formally, the trading network is an instance of the model ofFleiner et al (2019), who incorporate income effects (and frictions) into the transferable-utility trading network model ofHatfield, Kominers, Nichifor, Ostrovsky, and Westkamp (2013).…”