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This paper proposes a non-cooperative game theoretical replica allocation technique (NCOR) to reduce user perceived Web access delays. NCOR uses distributed agents that because of their local knowledge act in a self-interested manner in order to enhance the performance of the servers that they represent. This can lead to some performance gains for some servers but has the potential to negatively impact the overall system's performance. NCOR uses an effective cost model to guarantee the overall system performance gain despite the self-interested actions of these agents. With spontaneous and non-deterministic strategies, the system can exhibit Nash equilibrium. However, that may or may not guaranteed system-wide performance at a given time. Furthermore, their can be multiple Nash equilibria, making it difficult to decide which one is the best. Instead, we use the notion of pure Nash equilibrium, which if achieved is guaranteed to ensure stable optimal performance. Pure Nash equilibrium can be only achieved by deterministic strategies. In general, the existence of a pure Nash equilibrium is remarkably hard to achieve; however, we prove the existence of such an equilibrium in NCOR. Experimental comparisons with several non-game theoretical techniques reveal that NCOR maintains superior solution quality, in terms of lower communication cost and reduced execution time.