In our previous work [2], we proposed a new concept of utility functions for rate control in communication networks. Unlike conventional utility-based rate control in which the utility function of each user is defined as a function of its transmitting data rate, in [2], we defined the utility function of each user as a function of not only its transmitting data rate but also it receiving data rate. The former is called a session-level utility function and the latter is called a user-level utility function. The user-level utility function reflects the satisfaction with the service of a user with two-way communication, which consists of transmitting and receiving sessions, better than the session-level utility function, since user's satisfaction depends on not only the satisfaction with its transmitting session but also that for its receiving session. In [2], an algorithm that required each user to know the exact utility function of its correspondent was developed. However, in some cases, this information might not be available due to some reasons such as security and privacy issues, and in such cases, the algorithm developed in [2] cannot be used. Hence, in this paper, we develop a new distributed algorithm that does not require each user to know the utility function of its correspondent. Numerical results show that our new algorithm, which does not require the utility information of the correspondent, converges to the same solution to that with the algorithm that requires the utility information of the correspondent.