This paper studies distributed cooperative multi-agent exploration methods in settings where the exploration is costly and the overall performance measure is determined by the minimum performance achieved by any of the individual agents. Such an exploration setting is applicable to various multi-agent systems, e.g., in Dynamic Spectrum Access exploration. The goal in such problems is to optimize the process as a whole, considering the tradeoffs between the quality of the solution obtained and the cost associated with the exploration and coordination between the agents. Through the analysis of the two extreme cases where coordination is completely free and when entirely disabled, we manage to extract the solution for the general case where coordination is taken to be costly, modeled as a fee that needs to be paid for each additional coordinated agent. The strategy structure for the general case is shown to be threshold-based, and the thresholds which are analytically derived in this paper can be calculated offline, resulting in a very low online computational load.