Matching with Externalities

Abstract

We incorporate externalities into the stable matching theory of two-sided markets. Extending the classical substitutes condition to allow for externalities, we establish that stable matchings exist when agent choices satisfy substitutability. In addition, we show that the standard insights of matching theory, like the existence of side-optimal stable matchings and the deferred acceptance algorithm, remain valid despite the presence of externalities even though the standard fixed-point techniques do not apply. Furthermore, we establish novel comparative statics on externalities.

Trading Networks With Frictions

“…First, to what extent can the condition that firms have bounded willingness to pay for trades be relaxed while still ensuring that trail-stable outcomes lift to competitive equilibria? Second, can externalities (as analyzed by Pycia and Yenmez (2017) and Rostek and Yoder (2018)) be incorporated into our analysis?…”

Assignment games with externalities revisited

“…This is an assumption of bounded rationality that, in essence, implies that agents expect almost everything to stay the same after blocking. As just discussed in relation to Pycia and Yenmez (2016), this is in contrast to our approach.…”

“…They find that, if choice functions are substitutable and satisfy "irrelevance of rejected alternatives", then stable outcomes (sets of contracts) exist. In contrast to our work, Pycia and Yenmez (2016) consider a notion of stability in line with Gale and Shapley (1962) in the sense that agents assume that their choices do not trigger reactions by the other agents. Instead, such predictions can be built into the choice functions.…”

“…However, as his notion of stability uses estimation functions in the spirit of Sasaki and Toda (1996), his result is subsumed by ours. Pycia and Yenmez (2016) examine externalities in a matching with contracts-setting. They find that, if choice functions are substitutable and satisfy "irrelevance of rejected alternatives", then stable outcomes (sets of contracts) exist.…”

Multiperiod Matching

“…Among these papers, is the closest to our setting and motivation. He proposes an alternative solution concept motivated by the literature on matching with externalities (Sasaki and Toda, 1996;Pycia and Yenmez, 2017). His proposal is neither weaker nor stronger than our definition of dynamic stability.…”