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Leadership Games with Convex Strategy Sets

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  • Bernhard von Stengel
  • Shmuel Zamir

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 leaders 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

  • Bernhard von Stengel & Shmuel Zamir, 2009. "Leadership Games with Convex Strategy Sets," Discussion Paper Series dp525, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp525
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    Cited by:

    1. Bernhard von Stengel, 2016. "Recursive Inspection Games," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 935-952, August.
    2. Jing Yang & Juan S. Borrero & Oleg A. Prokopyev & Denis Sauré, 2021. "Sequential Shortest Path Interdiction with Incomplete Information and Limited Feedback," Decision Analysis, INFORMS, vol. 18(3), pages 218-244, September.
    3. 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.
    4. Balkenborg, Dieter G. & Hofbauer, Josef & Kuzmics, Christoph, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, vol. 8(1), January.
    5. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.
    6. Stefanos Leonardos & Costis Melolidakis, 2018. "On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-28, September.
    7. 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".
    8. Yunjian Xu & Katrina Ligett, 2018. "Commitment in first-price auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 449-489, August.
    9. Nicola Basilico & Stefano Coniglio & Nicola Gatti & Alberto Marchesi, 2020. "Bilevel programming methods for computing single-leader-multi-follower equilibria in normal-form and polymatrix games," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 3-31, March.
    10. Guzmán, Cristóbal & Riffo, Javiera & Telha, Claudio & Van Vyve, Mathieu, 2022. "A sequential Stackelberg game for dynamic inspection problems," European Journal of Operational Research, Elsevier, vol. 302(2), pages 727-739.
    11. Guzman, Cristobal & Riffo, Javiera & Telha, Claudio & Van Vyve, Mathieu, 2021. "A Sequential Stackelberg Game for Dynamic Inspection Problems," LIDAM Discussion Papers CORE 2021036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Zhengqiu Zhu & Bin Chen & Genserik Reniers & Laobing Zhang & Sihang Qiu & Xiaogang Qiu, 2017. "Playing Chemical Plant Environmental Protection Games with Historical Monitoring Data," IJERPH, MDPI, vol. 14(10), pages 1-23, September.
    13. Edward JM Colbert & Alexander Kott & Lawrence P Knachel, 2020. "The game-theoretic model and experimental investigation of cyber wargaming," The Journal of Defense Modeling and Simulation, , vol. 17(1), pages 21-38, January.

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    JEL classification:

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

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