Abstract
The single-dipped domain can be used to model any allocation problem where a single output must be chosen in an interval with the assumption that agents’ preferences have a single most loathful point (the dip) in the interval, and the preferences are increasing as one moves away from that dip. Practical domains like this appear in political voting system where each voter has his most-hated candidate and alternative candidates are evaluated by their proximity to this candidate or in obnoxious location problem, where each agent prefers to have the obnoxious location to be distant from his own location, among others. We first characterize deterministic and anonymous strategy-proof and group strategy-proof mechanisms on single-dipped public policy domain, complementing the well-known results on single-peaked policy domain first investigated by Moulin (Pub. Choice 35:437–455, 1980). Then we consider the tradeoff between strategy-proofness and efficiency by applying our characterization. As concrete applications of our results, we extend existing models and results, and resolve several open questions related to the obnoxious facility location game from the algorithmic mechanism design literature.
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References
Arrow, K.J.: A difficulty in the concept of social welfare. J. Polit. Theory 58(4), 328–346 (1950)
Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: Strategyproof approximation of the minimax on networks. Math. Oper. Res. 35, 513–526 (2010)
An, M.Y.: Log-concave probability distributions: theory and statistical testing. Working Paper, Duke University (1995)
Ashlagi, I., Fischer, F., Kash, I., Procaccia, A.D.: Mix and match. In: Proceedings of ACM-EC, vol. 99, pp. 305–314 (2010)
Barberà, S., Berga, D., Moreno, B.: Individual versus group strategy-proofness: when do they coincide? J. Econ. Theory 145(5), 1648–1674 (2010)
Barberà, S., Berga, D., Moreno, B.: Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results. Int. J. Game Theory 41(4), 791–808 (2012)
Barberà, S., Berga, D., Moreno, B.: Domains, ranges and strategy-proofness: the case of single-dipped preferences. Soc. Choice Welf. 39(2–3), 335–352 (2012)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Brandt, F., Conitzer, V., Endriss, U.: Computational social choice. In: Weiss, G. (ed.) Multiagent Systems, pp. 213–283. MIT Press, Cambridge (2012)
Cheng, Y., Yu, W., Zhang, G.: Strategy-proof approximation mechanisms for obnoxious facility game on networks. Theor. Comput. Sci. 497, 154–163 (2011)
Dughmi, S., Ghosh, A.: Truthful assignment without money. In: Proceedings of ACM-EC, pp. 325–334 (2010)
Gibbard, A.: Manipulation of voting schemes: a general result. Econom. J. Econom. Soc. 41, 587–601 (1973)
Garman, M.B., Kamien, M.I.: The paradox of voting: probability calculations. Syst. Res. Behav. Sci. 13(4), 306–316 (1968)
Guo, M., Conitzer, V.: Strategy-proof allocation of multiple items between two agents without payments or priors. In: Proceedings of AAMAS, pp. 881–888 (2010)
Guo, M., Conitzer, V., Reeves, D.: Competitive repeated allocation without payments. In: Proceedings of WINE, pp. 244–255 (2010)
Holcombe, R.G.: Public Sector Economics: The Role of Government in the American Economy. Prentice Hall, Upper Saddle River (2006)
Harrenstein, P., de Weerdt, M.M., Conitzer, V.: A qualitative Vickrey auction. In: Proceedings of ACM-EC, pp. 197–206 (2009)
Ibara, K., Nagamochi, H.: Characterizing mechanisms in obnoxious facility game. Working Paper, Kyoto University (2012)
Klaus, B., Petters, H., Storchen, T.: Strategy-proof division of a private good when preferences are single-dipped. Econ.Lett. 55(3), 339–346 (1997)
Lu, P., Sun, X., Wang, Y., Zhu, Z.A.: Asymptotically optimal strategy-proof mechanisms for two-facility games. In: Proceedings of AMC-EC, pp. 315–324 (2010)
Lu, P., Wang, Y., Zhou, Y.: Tighter bounds for facility games. In: Proceedings of WINE, pp. 137–148 (2009)
May, K.O.: A set of independent necessary and sufficient conditions for simple majority decision. Econom. J. Econom. Soc. 20, 680–684 (1952)
Manjunath, V.: Efficient and strategy-proof social choice when preferences are single-dipped. Int. J. Game Theory 43, 579–597 (2010)
Manjunath, V.: Group strategy-proofness and social choice between two alternatives. Math. Soc. Sci. 63, 239–242 (2011)
Meir, R., Almagor, S., Michaely, A., Rosenschein, J.S.: Tight bounds for strategyproof classification. In: Proceedings of AAMAS, pp. 319–326 (2011)
Meir, R., Procaccia, A.D., Rosenschein, J.S.: Strategyproof classification with shared inputs. In: Proceedings of IJCAI. 220–225 (2009)
Meir, R., Procaccia, A.D., Rosenschein, J.S.: On the limits of dictatorial classification. In: Proceedings of AAMAS, pp. 609–616 (2010)
Moulin, H.: On strategy-proofness and single peakedness. Pub. Choice 35(40), 437–455 (1980)
Nisan, N.: Introduction to mechanism design (for computer scuentists). In: Nisan, N., Roughgarden, T., Tardös, E., Vazirani, V.V. (eds.) Algorithmic Game Theory, pp. 209–241. Cambridge University Press, Cambridge (2007)
Othman, A., Budish, E., Sandholm, T.: Finding approximate competitive equilibria: Efficient and fair course allocation. In: Proceedings of AAMAS, pp. 873–880 (2010)
Peremans, W., Storcken, T.: Strategy-proofness on the single-dipped preference domain. In: Proceedings of ICLP, pp. 296–313 (1999)
Peters, D., Lackner, M.: Preferences Single-Peaked on a Circle. AAAI. (2017)
Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of ACM-EC, pp. 177–186 (2009)
Satterthwaite, M.A.: Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econ. Theory 10(2), 187–217 (1975)
Schmmer, J., Vohra, R.: Mechanism design without money. In: Nisan, N., Roughgarden, T., Tardös, E., Vazirani, V.V. (eds.) Algorithmic Game Theory, pp. 243–264. Cambridge University Press, Cambridge (2007)
Acknowledgements
The first author’s research is supported by the National Natural Science Foundation of China (NSFC grants 11771386 and 11728104) and First Class Discipline A of Zhejiang for Statistics in Zhejiang University of Finance and Economics. The second author’s research is supported by the Natural Science and Engineering Research Council of Canada (NSERC grant 06446) and the National Natural Science Foundation of China (NSFC grant 11728104). The third and fourth authors’ research is supported by the National Natural Science Foundation of China (NSFC grant 11531014). Particularly, we acknowledge the two anonymous referees for their constructive comments to improve the presentation of this paper.
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Han, Q., Du, D., Xu, D. et al. Approximate efficiency and strategy-proofness for moneyless mechanisms on single-dipped policy domain. J Glob Optim 70, 859–873 (2018). https://doi.org/10.1007/s10898-017-0586-x
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DOI: https://doi.org/10.1007/s10898-017-0586-x