That does sound like a noncooperative choice of strategies, and one that might be usefully modeled by a Nash equilibrium. The quick-and-obvious guess is that strategic resource demands might be a dominant strategy, so that a prisoner's dilemma-like model might apply. Sometimes the obvious answer is the correct one. But, on the other hand, have you actual evidence that the tenants are increasing their resource demands for that reason? Even if there are no "competing business interests," noncooperative tenants would ignore the costs to other tenants from the congestion they create, resulting in an externality. This is still a noncooperative game model, but might be addressed by congestion pricing on the part of the data center supplier, and economists (perhaps more than game theorists per se) understand congestion pricing pretty well.

This scenario calls for the use of the Market Paradigm (http://www.ssrn.com/abstract=437181), which could help to identify the unfolding states of cooperative and non-cooperative tendencies by users of a common resource(s).

There can be two (or more) situations.

1) In case when tenants declare there max demand of resources, one can simply apply banker's algorithm for allocating resources, an algorithm that is commonly studied & applied in case of operating systems for allocating resources. In this case, one may not assume that tenants are with competing interests. They request a resource because they need it. It is implicit that they do not have competing interests.

2) In case, they have competing interests, a tenant may request a resource even if he/she does not need it. (For example, one may request a resource, because holding it may possess some benefits e.g. one perceived benefit can be that the resource will not then be allocated to the competitor.) In such a case, where tenants have competing interests, and they perceive that allocation of resources is probabilistic and may incur a cost or benefits, one may apply game theory. Further, depending upon the situations, one may go for either cooperative games or non-cooperative games.

The main problem might be model the profits/losses of each individual as a function of 1) the resources available to complete its own tasks and 2) the success/failure of an opponent to complete its tasks. This in an interesting and realistic scenario.

For example, if two players are in a contest to solve the same problem, the game can be seen as a zero sum game, in which the player that solves the problem first is the winner. However, there might be rules in the resource allocation process that makes the problem more complex. In any case, this scenario might not be too realistic.

The responses you have so far elicited (and your own question) assume that game theory offers a suitable framework for the analysis of such a situation.  Might I suggest that you consider instead the application of drama theory (for more information look perhaps at the archive of applications at www.dilemmasgalore.com) which in my view offers a much more realistic approach for practical interventions