In a general equilibrium framework where buyers and sellers do not meet automatically but search each other, it becomes a strategic choice whether to search for a partner or wait for a partner. We study the question whether to search or wait in random matching models where trades are consummated either in auctions or in bargaining, and we determine their Nash equilibria.
Most search models assume that either buyers or sellers search. Burdett, Coles, Kiyotaki and Wright (1995 AER) endogenise the search decision in a model of fiat money and explicit search costs. Herreiner (1999 discussion paper B-462, University of Bonn) studies a market similar to ours, but she ignores price formation that is central in our model.
The matching process in our model is of urn-ball type or many-to-one, with no explicit search costs. We ignore the co-ordination aspect where only one type searches, since everyone expects this type to search. Instead, we consider a mixed strategy equilibrium where both buyers and sellers can search and wait, and we find that it exists for a large interval of parameter values. The mixed strategy tells the likelihood of searching versus waiting for buyers and sellers, and it provides insight into the relevance of standard practice of postulating the identity of searchers and waiters. We investigate different mechanisms of price determination, including auction and bargaining. The main result is that the more numerous party searches.
We also determine the equilibrium of, to our knowledge, a new setup where buyers and sellers are in locations. When a, say, seller decides to search, his location becomes empty and a searching, say, buyer may contact this empty location.
This can be thought to depict an environment of very little co-ordination where agents on both sides of the market may end up without a partner, unlike in the basic model. We compare the efficiency of the above models to this model. This is done numerically.
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