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Replicating data objects onto servers across a system can alleviate access delays. The selection of data objects and servers requires solving a constraint optimization problem, which is NP-complete in general. A majority of conventional replica placement techniques falter on issues of scalability or solution quality. To counteract such issues, we propose a game theoretical replica placement technique, in which computational agents compete for the allocation or reallocation of replicas onto their servers in order to reduce the user perceived access delays. The technique is based upon six well-defined axioms, each guaranteeing certain basic game theoretical properties. This eccentric method of designing game theoretical techniques using axioms is unique in the literature and takes away from the designers the cumbersome mathematical details of game theory. The distinctive feature of these axioms is that when amassed together, their individual properties constrict into one system-wide performance enhancement property, which in our case is the reduction of access time. The control of the proposed technique is "semi-distributed" in nature, wherein all the heavy processing is done on the servers of the distributed system and the central body is only required to take a binary decision: (0) not to replicate or (1) to replicate. This semi-distributed approach makes the technique scalable and helps solutions to converge in a fast turn-around time without loosing much of the solution quality. Experimental comparisons are made against: 1) branch and bound, 2) greedy, 3) genetic, 4) Dutch auction, and 5) English auction. As attested by the results, the proposed technique maintains superior solution quality in terms of lower communication cost and reduced execution time.