A Walrasian Rubinstein and Wolinsky model

We provide a full dynamic analysis of a continuous-time variant of Rubinstein and Wolinsky (1985) matching and bargaining model with unbalanced flows of buyers and sellers. The focus is on the price limit as the frictions of search are removed. It is found that a necessary and sufficient condition for the limit price to be Walrasian at all times is the alignment of the initial buyer and seller stocks with the flows.     

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

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-it-or-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.     

The role of private information in dynamic matching and bargaining: Can it be good for efficiency?

We consider a private information replica of the dynamic matching and bargaining model of Mortensen and Wright (2002). We find that private information typically deters entry. But, the welfare can actually be higher under private information.     

FOR‐PROFIT SEARCH PLATFORMS

We consider optimal pricing by a profit‐maximizing platform running a dynamic search and matching market. Buyers and sellers enter in cohorts over time, meet, and bargain under private information. The optimal centralized mechanism, which involves posting a bid–ask spread, can be decentralized through participation fees charged by the intermediary to both sides. The sum of buyers' and sellers' fees equals the sum of inverse hazard rates of the marginal types, and their ratio equals the ratio of buyers' and sellers' bargaining weights. We also show that a monopolistic intermediary in a search market may be welfare enhancing.