Limitations of cross-monotonic cost-sharing schemes

A cost-sharing scheme is a set of rules defining how to share the cost of a service (often computed by solving a combinatorial optimization problem) amongst serviced customers. A cost-sharing scheme is cross-monotonic if it satisfies the property that everyone is better off when the set of people who receive the service expands. In this paper, we develop a novel technique for proving upper bounds on the budget-balance factor of cross-monotonic cost-sharing schemes. We apply this technique to games defined based on several combinatorial optimization problems including the problems of edge cover, vertex cover, set cover, and metric facility location, and in each case derive tight or nearly-tight bounds. In particular, we show that for the facility location game, there is no cross-monotonic cost-sharing scheme that recovers more than a third of the total cost. This result together with a recent 1/3-budget-balanced cross-monotonic cost-sharing scheme of P

• Type: Journal
• Year: 2008
• Where: TALG
• Authors: Nicole Immorlica, Mohammad Mahdian, Vahab S. Mirrokni
• Keywords: Combinatorial Optimization Problems, Cost-sharing Schemes, Cross-monotonic Cost-sharing Schemes, TALG 2008