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

Abstract

We study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information. A friction parameter is τ , the length of the time period until the next meeting. We provide a necessary and sufficient condition for the convergence of mechanism outcomes to perfect competition at the linear rate in τ , which is shown to be the fastest possible among all bargaining mechanisms. The condition requires that buyers and sellers always retain some bargaining power. The bargaining mechanisms that satisfy this condition are called nonvanishing bargaining power (NBP) mechanisms. Simple random proposer take-itor-leave-it protocols are NBP, while k-double auctions (k-DA) are not. We find that k-DAs have equilibria that converge to perfect competition at a linear rate, converge at a slower rate or even do not converge at all.

Bilateral matching and bargaining with private information

“…The literature on costly search, including Satterthwaite and Shneyerov (2007), Shneyerov and Wong (2008) and Atakan (2008), has focused on small frictions and convergence to perfect competition. 4 Gale (1987) assumes symmetric bargaining power and does not address the existence of a nontrivial equilibrium.…”

“…Satterthwaite and Shneyerov (2007) consider firstprice auctions. Shneyerov and Wong (2008) study convergence to perfect competition of general matching and bargaining mechanisms, including the mechanism considered here. For fixed α B and α S , Shneyerov and Wong (2008) show that, as the frictions (κ B , κ S , r) → 0, all equilibria converge to perfect competition, and do so at the optimal rate.…”

Inefficiency caused by random matching and heterogeneity

“…They also find that under some conditions private information may contribute to the efficiency of the markets. 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.…”

Dynamic matching and bargaining with heterogeneous deadlines

“…Exceptions are, among others, Merlo and Wilson (1995) in an environment where the bargaining set changes over time in a stochastic manner and Fershtman and Seidmann (1993) who allow for endogenous commitments to not accept proposals that are worse than previously rejected proposals. 6 For exceptions, see Serrano (2002) and Shneyerov and Wong (2010a). zero cost and all buyers have unitary demands for this good, which they all value at one.…”