Stability and Competitive Equilibrium in Trading Networks

Abstract

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Matching in Networks with Bilateral Contracts

“…Problems of this form often arise in contracting relationships, and they have a well-known solution, albeit one outside the scope of classical matching theory. One resolution to this dilemma dates back to ideas of Vickrey (1961) and Pigou: firm f 1 should pay a transfer to f 2 equal to the value of the externality f 1 causes by dropping contract x 1 in favor of y. Generalizing this intuition, Hatfield et al (2011) find that transferable utility promotes stability in some new settings. Even with transferable utility, full substitutability is necessary in order to guarantee the existence of stable allocations (Hatfield et al (2011)).…”

“…One resolution to this dilemma dates back to ideas of Vickrey (1961) and Pigou: firm f 1 should pay a transfer to f 2 equal to the value of the externality f 1 causes by dropping contract x 1 in favor of y. Generalizing this intuition, Hatfield et al (2011) find that transferable utility promotes stability in some new settings. Even with transferable utility, full substitutability is necessary in order to guarantee the existence of stable allocations (Hatfield et al (2011)). However, many problems naturally generate complementarities; a hospital may open a new wing only if it acquires doctors of multiple specialities, or a firm may be able to operate more efficiently with more units.…”

On Stable Matchings and Flows

“…They constructed a special stable marriage scheme with the help of a finite procedure, the so-called deferred acceptance algorithm. It also turned out that for the existence of a stable scheme, it is not necessary that the number of men is the same as the number of women or that After the original versions of our present work ( [7,8]), Hatfield et al generalized the Hatfield-Kominers result [6] in [9] to a "half-discrete" model (prices are arbitrary, but trading is done with integral amounts of goods) that allows cycles. The authors claim that under full substitutable preferences, there always exists a competitive equilibrium that corresponds to a stable outcome.…”

Strategic Models of Intermediation Networks

“…In this case, the value of the object to the final buyers depends on who provides intermediate inputs, and the network describes how inputs from upstream firms can be combined with inputs of downstream firms. 3 Recent work in economics has focused on the optimal allocation of ownership rights along a supply chain, and on stable contracts along supply chains, e.g., Antras and Chor (2013), Ostrovsky (2008) and Hatfield et al (2013). Some other work has focused, instead, on the role that production supply chains play in translating idiosyncratic shocks into volatility at the aggregate level, e.g., Acemoglu et al (2012).…”