This paper analyses Nash equilibria of a sealed offer bargaining game where agents first choose their optimal trading sides before they begin bargaining. In a full-participation Nash equilibrium, the probability of any trader reaching an agreement at the bargaining stage will be higher than that obtained in bargaining models with exogenously fixed sides. However, owing to the additional uncertainty of finding a trading partner, the probability of successful trading will be reduced. The model also shows that some high (low) valuation agents will always be buyers (sellers) even if the pricing rule is fully biased against them. Furthermore, in a partial-participation equilibrium, when the participation cost for a particular side increases, the number of participants decreases not only in that particular side, but also in the entire market.