Competitive Equilibria in Decentralized Matching With Incomplete Information

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may Abstract.This paper shows that all perfect Bayesian equilibria of a decentralized dynamic matching market with two-sided incomplete information of independent private values variety converge to competitive equilibria. Each buyer wants to purchase a bundle of heterogeneous, indivisible goods and each seller owns one unit of a heterogeneous indivisible good (as in Kelso and Crawford (1982) or Gul and Stacchetti (1999)). Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through bilateral bargaining between buyers and sellers. The paper considers a market in steady state. It is shown that as frictions, i.e., discounting and fixed costs of search become small, all equilibria of the market game converge to perfectly competitive equilibria.

Inefficiency caused by random matching and heterogeneity

“…This hints that reducing the costs of entry may actually decrease the gains from trade in markets with frictions. Similar kinds of results are found in Atakan (2008) and Shneyerov and Wong (2008a) but it should be borne in mind that they focus on limit economies.…”

“…Shneyerov and Wong (2008b) show that there is convergence to a Walrasian outcome when bilateral bargaining in decentralised markets is of the type where both parties have a strictly positive probability of making a take-it-or-leave-it offer. Atakan (2008) shows convergence to a Walrasian outcome in a model with two-sided private information where buyers search for a bundle of goods. In his model meetings are bilateral, and the proposals consist of mechanisms rather than just prices.…”

Bilateral matching and bargaining with private information

“…The Diamond effect can severely restrict efficiency of the market even with small frictions. Atakan (2009) also considers a DMBG with costly search, with a focus on convergence to perfect competition. 5 He proves a general existence result assuming Free First Draw (FD): the sellers with cost below some small ε must enter for at least 4 Dynamic matching models have also been used to study markets for durable goods, as in Inderst and Müller (2002), or to study screening, as in Inderst (2001).…”

The rate of convergence to perfect competition of matching and bargaining mechanisms

“…(Satterthwaite and Shneyerov (2007) restrict attention to auctions.) Atakan (2008) provides an important extension of the results of Satterthwaite and Shneyerov (2007) to multiple units and allows each trader to be a proposer with certain probability. Atakan (2008) allows the proposers to offer direct bargaining mechanisms (DMBs, as defined in Myerson and Satterthwaite (1983)), and shows that in equilibrium they can do no better than simply make price offers.…”