Game theory is adapted to a variety of domains such as economics, biology, engineering, political science, computer science, and philosophy in order to analyze economic behaviors. This research is an application of game theory to wireless communication. In particular, in terms of bargaining game we dealt with a multimedia resource allocation problem in wireless communication, which is rapidly spreading such as Wibro, WCDML, IPTV, etc. The algorithm is assumed to allocate multimedia resources to users who can choose and access differentiated media services. For this purpose, 3 utility function of users is devised to reflect quality of service (QoS) and price. We illustrated experimental results with synthesis data which were made to mimic real multimedia data, and analyzed differentiated service providing and the effect of the utility function.