Directed Multilateral Matching in a Monetary Economy
We consider a monetary economy with directed multilateral matching between buyers and sellers. A buyer chooses how much money to hold, observes the location of all sellers, and decides which seller to visit. The number of buyers that arrive at a particular seller is random due to lack of coordination. Every seller has a single indivisible good and all buyers have the same valuation for the good, though they may hold different amounts of money. The good is allocated according to a second price auction where buyers bid with their money rather than valuations. We show that in equilibrium ex ante identical buyers choose different money holdings: carrying more money is costly but it increases the probability of winning the auction. The unique equilibrium distribution of money holdings is analytically characterized. The entry of sellers is efficient at the Friedman rule but is suboptimal for higher inflation rates
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