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In this paper, we consider a decentralized approach to the multi-agent target assignment problem and explore the deterioration of the quality of assignment solution in respect to the decrease of the quantity of the information exchanged among communicating agents and their communication range when the latter is not sufficient to maintain the connected communication graph. The assignment is achieved through a dynamic iterative auction algorithm in which agents (robots) assign the targets and move towards them in each period. In the case of static targets and connected communication graph, the algorithm results in an optimal assignment solution. The assignment results are compared with two benchmark cases: a centralized one in which all the global information is known and therefore, the optimal assignment can be found, and the greedy one in which each agent moves towards the target with the highest benefit without communication with any other agent.