ABSTRACT
The literature on algorithmic mechanism design is mostly concerned with game-theoretic versions of optimization problems to which standard economic money-based mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforcing payments. In this paper, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We argue that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are ubiquitous, and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity.
We present a case study in approximate mechanism design without money. In our basic setting agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost, and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located, and a domain where each agent controls multiple locations.
- N. Andelman, Y. Azar, and M. Sorani. Truthful approximation mechanisms for scheduling selfish related machines. In Proc. of 22nd STACS, pages 69--82, 2005. Google ScholarDigital Library
- A. Archer and E. Tardos. Truthful mechanisms for one-parameter agents. In Proc. of 42nd FOCS, pages 482--491, 2001. Google ScholarDigital Library
- A. Archer and E. Tardos. Frugal path mechanisms. ACM Transactions on Algorithms, 3(1), article 3, 2007. Google ScholarDigital Library
- S. Arora, P. Raghavan, and S. Rao. Approximation schemes for Euclidean k-medians and related problems. In Proc. of 30th STOC, pages 106--113, 1998. Google ScholarDigital Library
- S. Barbera. An introduction to strategy-proof social choice functions. Social Choice and Welfare, 18:619--653, 2001.Google ScholarCross Ref
- S. Barbera and B. Peleg. Strategy-proof voting schemes with continuous preferences. Social Choice and Welfare, 7:31--38, 1990.Google ScholarCross Ref
- M. Bern and D. Eppstein. Approximation algorithms for geometric problems. In D. Hochbaum, editor, Approximation Algorithms for NP-Hard Problems. PWS Publishing, 1996. Google ScholarDigital Library
- G. Christodoulou, E. Koutsoupias, and A. Vidali. A lower bound for scheduling mechanisms. In Proc. of 18th SODA, pages 1163--1170, 2007. Google ScholarDigital Library
- O. Dekel, F. Fischer, and A.D. Procaccia. Incentive compatible regression learning. In Proc. of 19th SODA, pages 277--286, 2008. Google ScholarDigital Library
- P. Dhangwatnotai, S. Dobzinski, S. Dughmi, and T. Roughgarden. Truthful approximation schemes for single-parameter agents. In Proc. of 49th FOCS, pages 15--24, 2008. Google ScholarDigital Library
- S. Dobzinski, N. Nisan, and M. Schapira. Truthful randomized mechanisms for combinatorial auctions. In Proc. of 38th STOC, pages 644--652, 2006. Google ScholarDigital Library
- E. Elkind, A. Sahai, and K. Steiglitz. Frugality in path auctions. In Proc. of 15th SODA, pages 701--709, 2004. Google ScholarDigital Library
- D. Gale and L.S. Shapley. College admissions and the stability of marriage. Americal Mathematical Monthly, 69(1):9--15, 1962.Google ScholarCross Ref
- A. Gibbard. Manipulation of voting schemes. Econometrica, 41:587--602, 1973.Google ScholarCross Ref
- R. Lavi and C. Swami. Truthful and near-optimal mechanism design via linear programming. In Proc. of 46th FOCS, pages 595--604, 2005. Google ScholarDigital Library
- R. Lavi and C. Swami. Truthful mechanism design for multi-dimensional scheduling via cycle monotonicity. In Proc. of 8th ACM-EC, pages 252--261, 2007. Google ScholarDigital Library
- D. Lehmann, L.I. O'Callaghan, and Y. Shoham. Truth revelation in rapid, approximately efficient combinatorial auctions. Journal of the ACM, 49(5):577--602, 2002. Google ScholarDigital Library
- S. Leonardi and G. Schäfer. Cross-monotonic cost-sharing methods for connected facility location. In Proc. of 5th ACM-EC, pages 242--243, 2004. Google ScholarDigital Library
- H. Levin, M. Schapira, and A. Zohar. Interdomain routing and games. In Proc. of 40th STOC, pages 57--66, 2008. Google ScholarDigital Library
- R. Meir, A.D. Procaccia, and J.S. Rosenschein. Strategyproof classification under constant hypotheses: A tale of two functions. In Proc. of 23rd AAAI, pages 126--131, 2008. Google ScholarDigital Library
- R. Meir, A.D. Procaccia, and J.S. Rosenschein. Strategyproof classification with shared inputs. In Proc. of 21st IJCAI, 2009. To appear. Google ScholarDigital Library
- E. Miyagawa. Locating libraries on a street. Social Choice and Welfare, 18(3):527--541, 2001.Google ScholarCross Ref
- H. Moulin. On strategy-proofness and single-peakedness. Public Choice, 35:437--455, 1980.Google ScholarCross Ref
- N. Nisan. Introduction to mechanism design (for computer scientists). In N. Nisan, T. Roughgarden, É. Tardos, and V. Vazirani, editors, Algorithmic Game Theory, chapter 9. Cambridge University Press, 2007.Google Scholar
- N. Nisan and A. Ronen. Algorithmic mechanism design. Games and Economic Behavior, 35(1-2):166--196, 2001.Google ScholarCross Ref
- M. Pal and E. Tardos. Group strategyproof mechanisms via primal-dual algorithms. In Proc. of 44th FOCS, pages 584--593, 2003. Google ScholarDigital Library
- A.D. Procaccia and M. Tennenholtz. Approximate mechanism design without money. Manuscript, 2009. Available from: http://www.cs.huji.ac.il/~arielpro/papers/facility.pdf.Google Scholar
- A.E. Roth and M. Sotomayor. Two-Sided Mathing: A Study in Game-Theoretic Modelling and Analysis. Cambridge University Press, 1991.Google Scholar
- M. Satterthwaite. Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10:187--217, 1975.Google ScholarCross Ref
- J. Schummer and R.V. Vohra. Strategy-proof location on a network. Journal of Economic Theory, 104(2):405--428, 2004.Google ScholarCross Ref
- J. Schummer and R.V. Vohra. Mechanism design without money. In N. Nisan, T. Roughgarden, É. Tardos, and V. Vazirani, editors, Algorithmic Game Theory, chapter 10. Cambridge University Press, 2007.Google Scholar
- Y. Sprumont. Strategyproof collective choice in economic and political environments. The Canadian Journal of Economics, 28(1):68--107, 1995.Google ScholarCross Ref
Index Terms
- Approximate mechanism design without money
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