Advertisement

Strategy-Proof Location Functions on Finite Graphs

  • F. R. McMorrisEmail author
  • Henry Martyn Mulder
  • Fred S. Roberts
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 92)

Abstract

A location function on a finite graph takes a set of most preferred locations (vertices of the graph) for a set of users, and returns a set of locations satisfying conditions meant to please the entire user set as much as possible. A strategy-proof location function is one for which it never benefits a user to report a suboptimal preferred location. We introduce four versions of strategy-proof and prove some preliminary results focusing on two well-known location functions, the median and the center.

Keywords

Location function Center Median Strategy-proof 

Notes

Acknowledgements

Fred Roberts thanks the National Science Foundation for support under grant SES-1024722 to Rutgers University and the Department of Homeland Security for support under award 2009-ST-061-CCI002-04 to Rutgers University.

References

  1. 1.
    Alon, N., Feldman, M., Procaccia A.D., Tennenholtz, M.: Strategyproof approximation of the minimax on networks. Math. Oper. Res. 35, 513–526 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Danilov, V.I.: The structure of non-manipulable social choice rules on a tree. Math. Soc. Sci. 27, 123–131 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Klavžar, S., Mulder, H.M.: Median graphs: characterizations, location theory, and related structures. J. Combin. Math. Combin. Comput. 30, 103–127 (1999)zbMATHMathSciNetGoogle Scholar
  4. 4.
    McMorris, F.R., Mulder, H.M., Roberts, F.S.: The median procedure on median graphs. Discrete Appl. Math. 84, 165–181 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    McMorris, F.R., Roberts, F.S., Wang, C.: The center function on trees. Networks 38, 84–87 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    McMorris, F.R., Mulder, H.M., Powers, R.C.: The median function on distributive semilattices. Discrete Appl. Math. 127, 319–324 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Miyagawa, E.: Locating libraries on a street. Soc. Choice Welf. 18, 527–541 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Moulin, H.: On strategy proofness and single peakedness. Public Choice 35, 437–455 (1980)CrossRefGoogle Scholar
  9. 9.
    Mulder, H.M.: The structure of median graphs. Discrete Math. 24, 197–204 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Mulder, H.M.: The Interval Function of a Graph, Mathematical Centre Tracts 132. Mathematisch Centrum, Amsterdam (1980)Google Scholar
  11. 11.
    Sanver, M.R.: Strategy-proofness of the plurality rule over restricted domains. Econ. Theory 39, 461–471 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Schummer, J., Vohra, R.V.: Strategy-proof location on a network. J. Econ. Theory 104, 405–428 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Taylor, A.D.: Social Choice and the Mathematics of Manipulation. Cambridge University Press, Cambridge (2005)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • F. R. McMorris
    • 1
    • 2
    Email author
  • Henry Martyn Mulder
    • 3
  • Fred S. Roberts
    • 4
  1. 1.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA
  2. 2.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  3. 3.Econometrisch InstituutErasmus UniversiteitRotterdamThe Netherlands
  4. 4.DIMACS Center, Rutgers UniversityPiscatawayUSA

Personalised recommendations