Cost Sharing for Connectivity with Budget

TL;DR

This paper addresses a cost sharing mechanism for connecting nodes in a graph, ensuring nodes are incentivized to cooperate and minimizing total connection costs despite strategic behavior.

Contribution

It introduces a novel cost sharing mechanism that incentivizes nodes to cooperate and prevents strategic edge cutting in network connectivity.

Findings

Designed mechanisms that incentivize cooperation among nodes.

Achieved minimized total connection costs.

Prevented strategic edge cutting behavior.

Abstract

We consider a cost sharing problem to connect all nodes in a weighted undirected graph, where the weight of each edge represents the cost to use the edge for the connectivity and the cost has to be shared among all connected nodes. There is one node called the source to which all the other nodes want to connect and it does not share the costs of the connectivity. As a node may need to go through other nodes to reach the source, the intermediate nodes may behave strategically to block the connection by cutting the edges adjacent to them. To prevent such strategical behavior, we design cost sharing mechanisms to incentivize all nodes not to cut any edge so that we can minimize the total cost for connecting all the nodes.