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We study a random matching economy, where the participants have Cobb-Douglas utility functions. At each time period
a pair of participants is selected and may choose to trade two goods. Under the appropriate symmetry conditions,
depending on the relation between the initial distribution of endowments and the agents preferences, we show that
the sequence of bilateral prices converges to the Walrasian price for this economy. Additionally, we study the effect of an asymmetry in the preferences on the difference between the bilateral price and the Walrasian price for this economy. We extend this model by associating a selfishness factor to each participant in this market. This brings up a game alike the prisoner`s dilemma. We discuss the effect of the selfishness on the increase in utility.
