IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v115y2019icp336-345.html
   My bibliography  Save this article

The duality gap for two-team zero-sum games

Author

Listed:
  • Schulman, Leonard J.
  • Vazirani, Umesh V.

Abstract

We consider multiplayer games in which the players fall in two teams of size k, with payoffs equal within, and of opposite sign across, the two teams. In the classical case of k=1, such zero-sum games possess a unique value, independent of order of play. However, this fails for all k>1; we can measure this failure by a duality gap, which quantifies the benefit of being the team to commit last to its strategy. We show that the gap equals 2(1−21−k) for m=2 and 2(1−m−(1−o(1))k) for m>2, with m being the size of the action space of each player. Extensions hold also for different-size teams and players with various-size action spaces.

Suggested Citation

  • Schulman, Leonard J. & Vazirani, Umesh V., 2019. "The duality gap for two-team zero-sum games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 336-345.
  • Handle: RePEc:eee:gamebe:v:115:y:2019:i:c:p:336-345
    DOI: 10.1016/j.geb.2019.03.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825619300466
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2019.03.011?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. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    2. Bin Wu & Julián García & Christoph Hauert & Arne Traulsen, 2013. "Extrapolating Weak Selection in Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 9(12), pages 1-7, December.
    3. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    4. J. Marschak, 1955. "Elements for a Theory of Teams," Management Science, INFORMS, vol. 1(2), pages 127-137, January.
    5. von Stengel, Bernhard & Koller, Daphne, 1997. "Team-Maxmin Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 309-321, October.
    Full references (including those not matched with items on IDEAS)

    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. Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 413-424, May.
    2. McAvoy, Alex & Fraiman, Nicolas & Hauert, Christoph & Wakeley, John & Nowak, Martin A., 2018. "Public goods games in populations with fluctuating size," Theoretical Population Biology, Elsevier, vol. 121(C), pages 72-84.
    3. von Stengel, Bernhard & Zamir, Shmuel, 2010. "Leadership games with convex strategy sets," Games and Economic Behavior, Elsevier, vol. 69(2), pages 446-457, July.
    4. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    5. Bin Wu & Lei Zhou, 2018. "Individualised aspiration dynamics: Calculation by proofs," PLOS Computational Biology, Public Library of Science, vol. 14(9), pages 1-15, September.
    6. Shun Kurokawa & Joe Yuichiro Wakano & Yasuo Ihara, 2018. "Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions," Games, MDPI, vol. 9(4), pages 1-24, December.
    7. Zhang, Libin & Yao, Zijun & Wu, Bin, 2021. "Calculating biodiversity under stochastic evolutionary dynamics," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    8. Alex McAvoy & Christoph Hauert, 2015. "Asymmetric Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-26, August.
    9. Alex McAvoy & Andrew Rao & Christoph Hauert, 2021. "Intriguing effects of selection intensity on the evolution of prosocial behaviors," PLOS Computational Biology, Public Library of Science, vol. 17(11), pages 1-21, November.
    10. Ehud Kalai & Eilon Solan, 2000. "Randomization and Simplification," Discussion Papers 1283, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Lau, Sau-Him Paul, 2001. "Aggregate Pattern of Time-dependent Adjustment Rules, II: Strategic Complementarity and Endogenous Nonsynchronization," Journal of Economic Theory, Elsevier, vol. 98(2), pages 199-231, June.
    12. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    13. Takuya Sekiguchi, 2023. "Fixation Probabilities of Strategies for Trimatrix Games and Their Applications to Triadic Conflict," Dynamic Games and Applications, Springer, vol. 13(3), pages 1005-1033, September.
    14. Van Damme, Eric, 2002. "Strategic equilibrium," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 41, pages 1521-1596, Elsevier.
    15. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    16. Konrad, Kai A. & Morath, Florian, 2020. "The Volunteer’s Dilemma in Finite Populations," CEPR Discussion Papers 15536, C.E.P.R. Discussion Papers.
    17. Konstantinos Georgalos & Indrajit Ray & Sonali SenGupta, 2020. "Nash versus coarse correlation," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1178-1204, December.
    18. M. Kleshnina & K. Kaveh & K. Chatterjee, 2020. "The role of behavioural plasticity in finite vs infinite populations," Papers 2009.13160, arXiv.org.
    19. Antonio Cabrales & Michalis Drouvelis & Zeynep Gurguy & Indrajit Ray, 2017. "Transparency is Overrated: Communicating in a Coordination Game with Private Information," CESifo Working Paper Series 6781, CESifo.
    20. Zhigang Cao, 2011. "Remarks on Bargaining and Cooperation in Strategic Form Games," Discussion Paper Series dp565, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

    More about this item

    Keywords

    Teams; Duality gap; Weak selection model;
    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:eee:gamebe:v:115:y:2019:i:c:p:336-345. 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/inca/622836 .

    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.