Approximation and Collusion in Multicast Cost Sharing 1 Aaron Archer 2 Cornell University, Operations Research Dept., Ithaca, NY 14853 E-mail: aarcher@orie.cornell.edu and Joan Feigenbaum 3 Arvind Krishnamurthy 4 Rahul Sami 5 Yale University, Computer Science Dept., New Haven, CT 06520-8285 E-mail: jf@cs.yale.edu, arvind@cs.yale.edu, sami@cs.yale.edu and Scott Shenker 6 ICSI, 1947 Center Street, Berkeley, CA 94704-1198 E-mail: shenker@icsi.berkeley.edu Version: November 2, 2002 Multicast routing is a technique for transmitting a packet from a single source to multiple receivers without wasting network bandwidth. To achieve transmission efficiency, multicast routing constructs a directed tree that connects the source to all the receivers and sends only one copy of the packet over each link of the directed tree. When a packet reaches a branch point in the tree, it is duplicated and a copy is sent over each downstream link. Multicasting large amounts of data to large groups of receivers is likely to incur significant costs, and these costs need to be covered by payments collected from the receivers. However, receivers cannot be charged more than what they are willing to pay, and the transmission costs of shared network links cannot be attributed to any single receiver. Thus, one must design cost-sharing mechanisms to determine which users receive the transmission and how much they are charged. Recent work in economics (Moulin and Shenker, 2001) leads naturally to the consideration of two mech- anisms: marginal cost (MC), which is efficient and strategyproof, and Shapley value (SH), which is budget- balanced and group-strategyproof and, among all mechanisms with these two properties, minimizes the worst-case welfare loss. Subsequent work in computer science shows that the MC mechanism can be com- puted by a simple, distributed algorithm that uses only two modest-sized messages per link of the multicast tree (Feigenbaum et al., 2001) but that computing the SH mechanism requires, in the worst case, that Ω(|P |) bits be sent over Ω(|N |) links, where P is the set of potential receivers, and N is the set of tree nodes (Feigen- baum et al., 2002). Here, we extend these results in two directions. First, we give a group-strategyproof mechanism that exhibits a tradeoff between the other properties of the Shapley value: It can be computed by an algorithm that is more communication-efficient than the natural SH algorithm (exponentially more so in the worst case), but it might fail to achieve exact budget balance or exact minimum welfare loss (albeit by 1 Abstract in Proceedings of the 3rd ACM Conference on Electronic Commerce, Tampa FL, October 2001. This work was supported by the DoD University Research Initiative (URI) program administered by the Office of Naval Research under Grant N00014-01-1-0795. 2 Supported by the Fannie and John Hertz Foundation. 3 Supported in part by ONR grants N00014-01-1-0795 and N00014-01-1-0447 and NSF grants CCR-0105337, CCR- TC-0208972, ANI-0207399, and ITR-0219018. 4 Supported in part by NSF grants CCR-9985304, ANI-0207399, and CCR-0209122. 5 Supported by NSF Career grant CCR-9702980 and ONR grant N00014-01-1-0795. 6 Supported in part by NSF grants ITR-0081698, ITR-0121555, and ANI-0207399. 1