IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v40y2011i1p147-177.html
   My bibliography  Save this article

Acyclicity of improvements in finite game forms

Author

Listed:
  • Nikolai Kukushkin

Abstract

Game forms are studied where the acyclicity, in a stronger or weaker sense, of (coalition or individual) improvements is ensured in all derivative games. In every game form generated by an ``ordered voting'' procedure, individual improvements converge to Nash equilibria if the players restrict themselves to ``minimal'' strategy changes. A complete description of game forms where all coalition improvement paths lead to strong equilibria is obtained: they are either dictatorial, or voting (or rather lobbing) about two outcomes. The restriction to minimal strategy changes ensures the convergence of coalition improvements to strong equilibria in every game form generated by a ``voting by veto'' procedure.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Nikolai Kukushkin, 2011. "Acyclicity of improvements in finite game forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 147-177, February.
    • Handle: RePEc:spr:jogath:v:40:y:2011:i:1:p:147-177
    DOI: 10.1007/s00182-010-0231-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-010-0231-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00182-010-0231-0?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
    2. Voorneveld, Mark & Norde, Henk, 1997. "A Characterization of Ordinal Potential Games," Games and Economic Behavior, Elsevier, vol. 19(2), pages 235-242, May.
    3. Nikolai Kukushkin, 2007. "Congestion games revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 57-83, September.
    4. Boros, E. & Gurvich, V., 2003. "On Nash-solvability in pure stationary strategies of finite games with perfect information which may have cycles," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 207-241, October.
    5. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    6. Voorneveld, M. & Norde, H.W., 1996. "A Characterization of Ordinal Potential Games," Other publications TiSEM a48550d5-29e7-48ec-b9d4-5, Tilburg University, School of Economics and Management.
    7. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 345-356.
    8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    9. Abdou, J., 1998. "Tight and Effectively Rectangular Game Forms: A Nash Solvable Class," Games and Economic Behavior, Elsevier, vol. 23(1), pages 1-11, April.
    10. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    11. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    12. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January.
    13. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    14. Kukushkin, Nikolai S, 1995. "Two-Person Game Forms Guaranteeing the Stability against Commitment and Delaying Tactics," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 37-48.
    15. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    16. Kukushkin, Nikolai S., 2002. "Perfect Information and Potential Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 306-317, February.
    17. Mariotti, Marco, 2000. "Maximum Games, Dominance Solvability, and Coordination," Games and Economic Behavior, Elsevier, vol. 31(1), pages 97-105, April.
    18. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    19. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
    20. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125, Elsevier.
    21. Mueller, Dennis C., 1978. "Voting by veto," Journal of Public Economics, Elsevier, vol. 10(1), pages 57-75, August.
    22. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    23. Friedman, James W. & Mezzetti, Claudio, 2001. "Learning in Games by Random Sampling," Journal of Economic Theory, Elsevier, vol. 98(1), pages 55-84, May.
    24. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    25. Peleg, Bezalel, 1978. "Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 153-161, January.
    26. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    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. Endre Boros & Ondřej Čepek & Vladimir Gurvich & Kazuhisa Makino, 2024. "Recognizing distributed approval voting forms and correspondences," Annals of Operations Research, Springer, vol. 336(3), pages 2091-2110, May.
    2. Stéphane Le Roux & Arno Pauly, 2020. "A Semi-Potential for Finite and Infinite Games in Extensive Form," Dynamic Games and Applications, Springer, vol. 10(1), pages 120-144, March.
    3. Novikova, Natalia M. & Pospelova, Irina I., 2017. "A lemma in open sequential voting by veto," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 141-144.
    4. Lihi Dery & Svetlana Obraztsova & Zinovi Rabinovich & Meir Kalech, 2019. "Lie on the Fly: Strategic Voting in an Iterative Preference Elicitation Process," Group Decision and Negotiation, Springer, vol. 28(6), pages 1077-1107, December.

    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. Kukushkin, Nikolai S., 2007. "Best response adaptation under dominance solvability," MPRA Paper 4108, University Library of Munich, Germany.
    2. Kukushkin, Nikolai S., 2010. "On continuous ordinal potential games," MPRA Paper 20713, University Library of Munich, Germany.
    3. Nikolai Kukushkin, 2011. "Nash equilibrium in compact-continuous games with a potential," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 387-392, May.
    4. Friedman, James W. & Mezzetti, Claudio, 2001. "Learning in Games by Random Sampling," Journal of Economic Theory, Elsevier, vol. 98(1), pages 55-84, May.
    5. Nikolai Kukushkin, 2007. "Congestion games revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 57-83, September.
    6. Kukushkin, Nikolai S., 2015. "Cournot tatonnement and potentials," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 117-127.
    7. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    8. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    9. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    10. Kukushkin, Nikolai S., 2014. "Strong equilibrium in games with common and complementary local utilities," MPRA Paper 55499, University Library of Munich, Germany.
    11. Kukushkin, Nikolai S., 2014. "Rosenthal's potential and a discrete version of the Debreu--Gorman Theorem," MPRA Paper 54171, University Library of Munich, Germany.
    12. Nikolai S Kukushkin, 2004. "'Strategic supplements' in games with polylinear interactions," Game Theory and Information 0411008, University Library of Munich, Germany, revised 28 Feb 2005.
    13. Kukushkin, Nikolai S., 2017. "Strong Nash equilibrium in games with common and complementary local utilities," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 1-12.
    14. Kukushkin, Nikolai S., 2018. "A universal construction generating potential games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 331-340.
    15. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    16. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    17. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    18. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
    19. Harks, Tobias & Klimm, Max, 2015. "Equilibria in a class of aggregative location games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 211-220.
    20. Hannu Salonen, 2013. "Utilitarian Preferences and Potential Games," Discussion Papers 85, Aboa Centre for Economics.

    More about this item

    Keywords

    Improvement dynamics; Game form; Perfect information; Potential game; Voting by veto; C72;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    Statistics

    Access and download statistics

    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:spr:jogath:v:40:y:2011:i:1:p:147-177. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.