We present in this paper a trust-based game theoretical model for Web services collaboration. The devised model is an application of the generic model about tasks allocation for agents, which is presented in [13]. We consider that a collaboration between Web services captures a possible interaction for achieving a specific task. We consider such collaboration as a game in which several Web services compete to win a task by bidding a cost for achieving it. The game winner is the Web service which has the minimal trust-based cost, which is the product of the cost and the inverse of the trust value of the bidding Web service. Initial trust values are computed based on the distance between the actual and the announced quality attribute values of a Web service. These values are computed during a collaboration evaluation period. They are updated after each game round based on a bayesian model. We show in this paper how the use of trust allows a safer collaboration between Web services with respect to collaborations where there is no consideration of the trust as a criteria for allocating tasks.