We design a laboratory experiment to study a decentralized matching market where agents (e.g. buyers and sellers) can engage in multiple transactions while keeping their valuations private. We compare the performance of four different market mechanisms to quantify the efficiency gains due to bargaining. We find that both sequential and simultaneous multi-lateral bargaining mechanisms boost efficiency (in terms of number of beneficial transactions, and the amount of money left on the table) relative to the benchmark case of a sealed-bid auction. We impute these results to the fact that agents follow a gradual 'bidding-up' strategy (e.g., Rubinstein 1982), which delays or precludes the discovery of beneficial transactions.
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