IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v69y2010i2p446-457.html
   My bibliography  Save this article

Leadership games with convex strategy sets

Author

Listed:
  • von Stengel, Bernhard
  • Zamir, Shmuel

Abstract

A basic model of commitment is to convert a two-player game in strategic form to a "leadership game" with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader's payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.

Suggested Citation

  • von Stengel, Bernhard & Zamir, Shmuel, 2010. "Leadership games with convex strategy sets," Games and Economic Behavior, Elsevier, vol. 69(2), pages 446-457, July.
  • Handle: RePEc:eee:gamebe:v:69:y:2010:i:2:p:446-457
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(09)00232-2
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    3. Reny, Philip J. & Robson, Arthur J., 2004. "Reinterpreting mixed strategy equilibria: a unification of the classical and Bayesian views," Games and Economic Behavior, Elsevier, vol. 48(2), pages 355-384, August.
    4. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," 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 45, pages 1723-1759 Elsevier.
    5. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
    6. Shapiro, Carl, 1989. "Theories of oligopoly behavior," Handbook of Industrial Organization,in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 6, pages 329-414 Elsevier.
    7. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    8. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
    9. von Stengel, Bernhard & Koller, Daphne, 1997. "Team-Maxmin Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 309-321, October.
    10. Avenhaus, Rudolf & Von Stengel, Bernhard & Zamir, Shmuel, 2002. "Inspection games," 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 51, pages 1947-1987 Elsevier.
    11. Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, 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. Bernhard von Stengel, 2016. "Recursive Inspection Games," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 935-952, August.
    2. Rabah Amir & Giuseppe Feo, 2014. "Endogenous timing in a mixed duopoly," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 629-658, August.
    3. Kuzmics, Christoph & Balkenborg, Dieter & Hofbauer, Josef, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, vol. 8(1), January.
    4. Cingiz, Kutay & Flesch, Janos & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2016. "Perfect Information Games where Each Player Acts Only Once," Research Memorandum 036, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Marco Marini & Giorgio Rodano, 2012. "Sequential vs Collusive Payoffs in Symmetric Duopoly Games," DIAG Technical Reports 2012-06, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".

    More about this item

    Keywords

    Commitment Correlated equilibrium First-mover advantage Follower Leader Stackelberg game;

    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:69:y:2010:i:2:p:446-457. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.