IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v61y2015icp144-151.html
   My bibliography  Save this article

Manipulation in games with multiple levels of output

Author

Listed:
  • Freixas, Josep
  • Parker, Cameron

Abstract

In (j,k)-games each player chooses amongst j ordered options and there are k possible outcomes. In this paper, we consider the case where players are assumed to prefer some outcomes to others, and note that when k>2 the players have an incentive to vote strategically. In doing so, we combine the theory of cooperative game theory with social choice theory, especially the theory of single-peaked preferences. We define the concept of a (j,k)-game with preferences and what it means for it to be manipulable by a player. We also consider Nash equilibriums with pure strategies for these games and find conditions that guarantee their existence.

Suggested Citation

  • Freixas, Josep & Parker, Cameron, 2015. "Manipulation in games with multiple levels of output," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 144-151.
    • Handle: RePEc:eee:mateco:v:61:y:2015:i:c:p:144-151
    DOI: 10.1016/j.jmateco.2015.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406815000981
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2015.08.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Roland Pongou & Bertrand Tchantcho & Lawrence Diffo Lambo, 2011. "Political influence in multi-choice institutions: cyclicity, anonymity, and transitivity," Theory and Decision, Springer, vol. 70(2), pages 157-178, February.
    2. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.
    3. Rabinowitz, George & Macdonald, Stuart Elaine, 1989. "A Directional Theory of Issue Voting," American Political Science Review, Cambridge University Press, vol. 83(1), pages 93-121, March.
    4. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    5. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    6. Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 399-431, December.
    7. Keith L. Dougherty & Julian Edward, 2010. "The Properties of Simple Vs. Absolute Majority Rule: Cases Where Absences and Abstentions Are Important," Journal of Theoretical Politics, , vol. 22(1), pages 85-122, January.
    8. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    9. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
    10. Rubinstein, Ariel, 1980. "Stability of decision systems under majority rule," Journal of Economic Theory, Elsevier, vol. 23(2), pages 150-159, October.
    11. Hirofumi Yamamura & Ryo Kawasaki, 2013. "Generalized average rules as stable Nash mechanisms to implement generalized median rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 815-832, March.
    12. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley–Shubik power index for dichotomous multi-type games," Theory and Decision, Springer, vol. 81(3), pages 413-426, September.
    2. Courtin, Sébastien & Nganmeni, Zéphirin & Tchantcho, Bertrand, 2017. "Dichotomous multi-type games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 9-17.
    3. Josep Freixas, 2022. "An Aggregation Rule Based on the Binomial Distribution," Mathematics, MDPI, vol. 10(23), pages 1-14, November.
    4. Josep Freixas & Montserrat Pons, 2021. "On anonymous and weighted voting systems," Theory and Decision, Springer, vol. 91(4), pages 477-491, November.
    5. Pongou, Roland & Tchantcho, Bertrand, 2021. "Round-robin political tournaments: Abstention, truthful equilibria, and effective power," Games and Economic Behavior, Elsevier, vol. 130(C), pages 331-351.
    6. Friedman, Jane & Parker, Cameron, 2018. "The conditional Shapley–Shubik measure for ternary voting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 379-390.
    7. Josep Freixas & Roberto Lucchetti, 2016. "Power in voting rules with abstention: an axiomatization of a two components power index," Annals of Operations Research, Springer, vol. 244(2), pages 455-474, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pongou, Roland & Tchantcho, Bertrand, 2021. "Round-robin political tournaments: Abstention, truthful equilibria, and effective power," Games and Economic Behavior, Elsevier, vol. 130(C), pages 331-351.
    2. Alaitz Artabe & Annick Laruelle & Federico Valenciano, 2012. "Preferences, actions and voting rules," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 15-28, March.
      • Artabe Echevarria, Alaitz & Laruelle, Annick & Valenciano Llovera, Federico, 2011. "Preferences, actions and voting rules," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    3. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    4. Freixas, Josep & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Achievable hierarchies in voting games with abstention," European Journal of Operational Research, Elsevier, vol. 236(1), pages 254-260.
    5. Josep Freixas & Montserrat Pons, 2021. "On anonymous and weighted voting systems," Theory and Decision, Springer, vol. 91(4), pages 477-491, November.
    6. Michael Müller & Clemens Puppe, 2023. "Strategy-proofness implies minimal participation under single-peakedness," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 131-151, April.
    7. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2021. "Influence in weighted committees," European Economic Review, Elsevier, vol. 132(C).
    8. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.
    9. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    10. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.
    11. Freixas, Josep, 2012. "Probabilistic power indices for voting rules with abstention," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 89-99.
    12. Qiaoming Han & Donglei Du & Dachuan Xu & Yicheng Xu, 2018. "Approximate efficiency and strategy-proofness for moneyless mechanisms on single-dipped policy domain," Journal of Global Optimization, Springer, vol. 70(4), pages 859-873, April.
    13. Joseph Armel Momo Kenfack & Bertrand Tchantcho & Bill Proces Tsague, 2019. "On the ordinal equivalence of the Jonhston, Banzhaf and Shapley–Shubik power indices for voting games with abstention," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 647-671, June.
    14. Guemmegne, Juliette T. & Pongou, Roland, 2014. "A policy-based rationalization of collective rules: Dimensionality, specialized houses, and decentralized authority," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 182-193.
    15. Gersbach, Hans & Tejada, Oriol, 2020. "Semi-flexible Majority Rules for Public Good Provision," CEPR Discussion Papers 15099, C.E.P.R. Discussion Papers.
    16. James Schummer, 1999. "Almost-dominant Strategy Implementation," Discussion Papers 1278, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Souvik Roy & Soumyarup Sadhukhan, 2019. "A characterization of random min–max domains and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 887-906, November.
    18. Donaldson, Jason & Piacentino, Giorgia & Malenko, Nadya, 2017. "Deadlock on the Board," CEPR Discussion Papers 12503, C.E.P.R. Discussion Papers.
    19. Roy, Souvik & Storcken, Ton, 2019. "A characterization of possibility domains in strategic voting," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 46-55.
    20. António Osório, 2020. "Performance Evaluation: Subjectivity, Bias and Judgment Style in Sport," Group Decision and Negotiation, Springer, vol. 29(4), pages 655-678, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:61:y:2015:i:c:p:144-151. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.