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This paper proposes a new distributed connection establishment scheme involving several competing network providers in a multimedia telecommunications environment. This connection establishment scheme, which is based on the concept of open competitive bidding, enables mutual selection by users and network providers. By employing this proposed scheme, both network providers and users can pursue their own objectives, according to their own bidding and awarding strategies. In this paper, a simple bidding strategy for network providers is presented, and the effectiveness of this strategy is evaluated by means of computer simulation. It is shown that each network provider can improve its profit by adopting this strategy. In this paper, an example of utility functions for users is presented, and the effectiveness of the mechanism with which users can select a network provider is also evaluated by means of computer simulation. Each user can improve his /her utility by selecting an appropriate network provider based on this utility function.