We report the results of two experiments on bilateral bargaining under the sealed-bid double auction mechanism in environments where theory calls for decidedly strategic play. The observed individual sellers' ask functions and buyers' bid functions, each based on 50 rounds of bargaining, are shown to be in good agreement with the Bayesian-Nash piecewise linear equilibrium solution of Chatterjee & Samuelson (1983). Although the game is played with random matching of traders on each round, both sellers and buyers change their behavior over time. The buyers in particular learn to bid more aggressively. The information sets of the two players are shown to be a major determinant of this result and of the strikingly disparate profits earned by buyer and seller during the experiment. To address the dynamics of this result, we propose a simple adaptive learning model postulating round-to-round changes in the entire bid/ask function which are proportional to the actual gain, if a deal was struck, or the gain that could have been but was not realized, if no agreement was reached on the previous round. Based on results from the experimental psychology literature, this model captures the major features of the mean bid/ask functions and accounts for most of the trial-to-trial variability in the buyers', but not the sellers', decisions. Copyright 1998 Academic Press.