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Ad hoc shared-ride systems built upon intelligent-transportation-system (ITS) technology represent a promising scenario for investigating the multicommodity-flow-over-time problem. This type of problem is known to be strongly NP-hard. Furthermore, capacity assignment in this shared-ride system is a problem to be solved in highly dynamic transportation and communication networks. So far, the known heuristics to this problem are centralized and require global knowledge about the environment. This paper develops a decentralized ad hoc capacity-assignment approach. Based on a spatial decomposition of the global optimization problem, the solution provides effective agent decisions using only local knowledge. The effectiveness is assessed by the trip quality for ride clients and by the required communication effort.