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This paper presents a game theory based technique for optimizing the bit rate control in video coding. Game theory, by virtue of its enormous potential for solving constrained optimization problems, has been effectively utilized in several branches of natural and social sciences. But this paper is the first attempt in using game theory for video compression. The objective is to optimize the perceptual quality while guaranteeing "fairness" in bit allocation among macroblocks (MBs). The proposed technique is a dual-level rate control algorithm: At the first level, the algorithm allocates the target bits to frames based on their coding complexity; a method to estimate the coding complexity of the remaining frames is proposed. At the second level, MBs of a frame play cooperative games such that each MB competes for a fair share of resources (bits) to optimize its quantization scale while considering the human visual system (HVS) perceptual property. We formulate the rate control problem by defining players, strategies and objective function. Since the whole frame is an entity perceived by viewers, MBs compete cooperatively under a global objective of achieving the best quality with the given bit constraint. The major advantage of the proposed approach is that the cooperative game leads to an optimal and fair bit allocation strategy based on the Nash bargaining solution. Another advantage is that it allows multi-objective optimization with multiple decision makers (e.g., MBs) in order to achieve accurate bit rate with good perceptual quality while maintaining a stable buffer level. Several extensions of the work are possible.