In this paper we analyze the process of allocating tasks to self-interested agents in uncertain changing open environments. The allocator in our model is responsible for the performance of dynamically arriving tasks using a second price reverse auction as the allocation protocol. Since the agents are self-interested (i.e. each agent attempts to maximize its own revenue), previous models concerning cooperative agents aiming for a joint goal are not applicable. Thus the main challenge is to identify a set of equilibrium strategies - a stable solution where no agent can benefit from changing its strategy given the other agents’ strategies - for any specific environmental settings. We formulate the model and discuss the difficulty in extracting the agents’ equilibrium strategies directly from the model’s equations. Consequently we propose an efficient algorithm to accurately approximate the agents’ equilibrium strategies. A comparative illustration through simulation of the system performance in a closed and open environments is given, emphasizing the advantage of the allocator operating in the latter environment, reaching results close to those obtained by a central enforceable allocation.