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We consider a multi-agent resource sharing problem that can be represented by a linear program. The amount of resource to be shared is fixed, and each agent adds to the linear cost and constraint a term that depends on some randomly extracted parameters, thus modelling heterogeneity among agents. We study the probability that the arrival of a new agent does not affect the optimal value and the resource share of the other agents, which means that the system cannot accommodate the request of adoi:10.1109/cdc.2017.8264226 dblp:conf/cdc/FalsoneMGP17 fatcat:xmvsqstexramjhvksc3alh5n4m