Abstract
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 can commonly be found in multi-agent systems, e.g., in multi-channel cooperative sensing where the quality of the overall connection is constrained by the individual qualities of the connections used by the different agents. 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. The methods considered in this paper differ in the level of coordination employed, ranging from no coordination to complete coordination. The strategy structure in all cases 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. The analysis is extended to the case where coordination is supplied by a self-interested monopolist communication provider, charging a fee that depends on the number of agents for which coordination is required. In this case, the agents' expected-benefit-maximizing cooperative exploration strategy is to have some sub-groups coordinate their exploration (if at all) while the remaining agents explore individually with no coordination between them. We show that given the option for side-payments, the exploring agents can improve their expected benefit by compensating the communication provider to change the price at which she offers her services. An illustration for the importance of considering others' findings in one's strategy is given using the spectrum sensing application, experimenting with real data.