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We consider a cost sharing problem on a weighted directed acyclic graph (DAG)with a source node to which all the other nodes want to connect. The cost(weight) of each edge is private information reported by multiple contractors,and among them, only one contractor is selected as the builder. All the nodesexcept for the source need to share the total cost of the used edges. However,they may block others' connections to the source by strategically cutting theiroutgoing edges to reduce their cost share, which may increase the total cost ofconnectivity. To minimize the total cost of connectivity, we design a costsharing mechanism to incentivize each node to offer all its outgoing edges andeach contractor to report all the edges' weights truthfully, and show theproperties of the proposed mechanism. In addition, our mechanism outperformsthe two benchmark mechanisms.

Cost Sharing under Private Costs and Connection Control on Directed Acyclic Graphs