Sharing the Cost of Multicast Transmissions

We investigate cost-sharing algorithms for multicast transmission. Economic considerations point to two distinct mechanisms, marginal cost and Shapley value, as the two solutions most appropriate in this context. We prove that the former has a natural algorithm that uses only two messages per link of the multicast tree, while we give evidence that the latter requires a quadratic total number of messages. We also show that the welfare value achieved by an optimal multicast tree is NP-hard to approximate within any constant factor, even for bounded-degree networks. The lower-bound proof for the Shapley value uses a novel algebraic technique for bounding from below the number of messages exchanged in a distributed computation; this technique may prove useful in other contexts as well.

[1]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[2]  M. Shubik.  Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing , 1962 .

[3]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[4]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[5]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[6]  Jerry R. Green,et al.  Partial Equilibrium Approach to the Free-Rider Problem , 1976 .

[7]  Nimrod Megiddo,et al.  Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree , 1978, Math. Oper. Res..

[8]  J. Laffont.  Aggregation and revelation of preferences , 1979 .

[9]  Jerry R. Green,et al.  Incentives in public decision-making , 1979 .

[10]  E. Maskin,et al.  The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility , 1979 .

[11]  Stefan Reichelstein,et al.  On the Informational Requirements for the Implementation of Social Choice Rules , 1981 .

[12]  E. Maskin.  The Theory of Implementation in Nash Equilibrium: A Survey , 1983 .

[13]  L. Hurwicz,et al.  Social goals and social organization : essays in memory of Elisha Pazner , 1985 .

[14]  Aurel A. Lazar,et al.  A Game Theoretic Approach to Decentralized Flow Control of Markovian Queueing Networks , 1987, Performance.

[15]  L. Shapley.  A Value for n-person Games , 1988 .

[16]  Beverly A. Sanders,et al.  An Incentive Compatible Flow Control Algorithm for Rate Allocation in Computer Networks , 1988, IEEE Trans. Computers.

[17]  Rahul Simha,et al.  A Microeconomic Approach to Optimal Resource Allocation in Distributed Computer Systems , 1989, IEEE Trans. Computers.

[18]  Donald F. Ferguson,et al.  An economy for flow control in computer networks , 1989, IEEE INFOCOM '89, Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies.

[19]  Scott Shenker,et al.  Efficient Network Allocations with Selfish Users , 1990, Performance.

[20]  Stephen E. Deering,et al.  Multicast routing in datagram internetworks and extended LANs , 1990, TOCS.

[21]  Paul Francis,et al.  Core based trees (CBT) , 1993, SIGCOMM 1993.

[22]  Paul Francis,et al.  Core based trees (CBT) , 1993, SIGCOMM '93.

[23]  Jeffrey S. Rosenschein,et al.  Rules of Encounter - Designing Conventions for Automated Negotiation among Computers , 1994 .

[24]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[25]  Herve C. Moulin,et al.  Incremental Cost Sharing: Characterization by Strategy Proofness , 1995 .

[26]  Scott Shenker,et al.  Making greed work in networks: a game-theoretic analysis of switch service disciplines , 1995, TNET.

[27]  Ariel Orda,et al.  Architecting noncooperative networks , 1995, Eighteenth Convention of Electrical and Electronics Engineers in Israel.

[28]  Deborah Estrin,et al.  The PIM architecture for wide-area multicast routing , 1996, TNET.

[29]  Eric J. Friedman,et al.  Learning and Implementation on the Internet , 1997 .

[30]  Craig Boutilier,et al.  Economic Principles of Multi-Agent Systems , 1997, Artif. Intell..

[31]  Michael Luck,et al.  Proceedings of the Third International Conference on Multi-Agent Systems , 1998 .

[32]  Michael P. Wellman,et al.  A market protocol for decentralized task allocation , 1998, Proceedings International Conference on Multi Agent Systems (Cat. No.98EX160).

[33]  Christophe Diot,et al.  Simple mu lticast: A design for sim-ple, low-overhead multicast , 1999 .

[34]  H. Moulin.  Incremental cost sharing: Characterization by coalition strategy-proofness , 1999 .

[35]  Noam Nisan,et al.  Algorithms for Selfish Agents , 1999, STACS.

[36]  David R. Cheriton,et al.  IP multicast channels: EXPRESS support for large-scale single-source applications , 1999, SIGCOMM '99.

[37]  Noam Nisan,et al.  Computationally feasible vcg-based mechanisms , 2000 .

[38]  David S. Johnson,et al.  The prize collecting Steiner tree problem: theory and practice , 2000, SODA '00.

[39]  H. Moulin,et al.  Strategyproof sharing of submodular costs:budget balance versus efficiency , 2001 .

[40]  Andrew V. Goldberg,et al.  Competitive auctions and digital goods , 2001, SODA '01.