IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v9y2018i3p42-d155312.html
   My bibliography  Save this article

The Optimal Strategy in the Minimum Effort Game

Author

Listed:
  • Edward Cartwright

    () (Department of Strategic Management and Marketing, Leicester Castle Business School, De Montfort University, Leicester LE1 9BH, UK)

Abstract

A simple expression is derived for the optimal strategy in the minimum effort game. This maps from player beliefs to an optimal effort level. From this expression the set of Nash equilibria in the game is fully characterized. All Nash equilibria are symmetric and involve at most two actions being played with positive probability. We discuss how our expression for the optimal strategy can help inform on the comparative statics of a change in the number of players and effort cost benefit ratio.

Suggested Citation

  • Edward Cartwright, 2018. "The Optimal Strategy in the Minimum Effort Game," Games, MDPI, Open Access Journal, vol. 9(3), pages 1-11, June.
  • Handle: RePEc:gam:jgames:v:9:y:2018:i:3:p:42-:d:155312
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/9/3/42/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2073-4336/9/3/42/
    Download Restriction: no

    References listed on IDEAS

    as
    1. Sebastian J. Goerg & Tibor Neugebauer & Abdolkarim Sadrieh, 2016. "Impulse Response Dynamics in Weakest Link Games," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 284-297, August.
    2. Jordi Brandts & David J. Cooper & Roberto A. Weber, 2015. "Legitimacy, Communication, and Leadership in the Turnaround Game," Management Science, INFORMS, vol. 61(11), pages 2627-2645, November.
    3. Jordi Brandts & David Cooper & Enrique Fatas, 2007. "Leadership and overcoming coordination failure with asymmetric costs," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 269-284, September.
    4. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    5. Giovanna Devetag & Andreas Ortmann, 2007. "When and why? A critical survey on coordination failure in the laboratory," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 331-344, September.
    6. Arno Riedl & Ingrid M. T. Rohde & Martin Strobel, 2016. "Efficient Coordination in Weakest-Link Games," Review of Economic Studies, Oxford University Press, vol. 83(2), pages 737-767.
    7. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, Oxford University Press, vol. 103(3), pages 441-463.
    8. Crawford, Vincent P, 1995. "Adaptive Dynamics in Coordination Games," Econometrica, Econometric Society, vol. 63(1), pages 103-143, January.
    9. Anderson, Simon P. & Goeree, Jacob K. & Holt, Charles A., 2001. "Minimum-Effort Coordination Games: Stochastic Potential and Logit Equilibrium," Games and Economic Behavior, Elsevier, vol. 34(2), pages 177-199, February.
    10. John Bryant, 1983. "A Simple Rational Expectations Keynes-type Model," The Quarterly Journal of Economics, Oxford University Press, vol. 98(3), pages 525-528.
    11. Jordi Brandts & David J. Cooper, 2006. "A Change Would Do You Good .... An Experimental Study on How to Overcome Coordination Failure in Organizations," American Economic Review, American Economic Association, vol. 96(3), pages 669-693, June.
    12. Crawford, Vincent & Broseta, Bruno, 1998. "What Price Coordination? The Efficiency-Enhancing Effect of Auctioning the Right to Play," American Economic Review, American Economic Association, vol. 88(1), pages 198-225, March.
    13. Dirk Engelmann & Hans-Theo Normann, 2010. "Maximum effort in the minimum-effort game," Experimental Economics, Springer;Economic Science Association, vol. 13(3), pages 249-259, September.
    14. Edward Cartwright & Joris Gillet & Mark Van Vugt, 2013. "Leadership By Example In The Weak-Link Game," Economic Inquiry, Western Economic Association International, vol. 51(4), pages 2028-2043, October.
    15. Ananish Chaudhuri & Tirnud Paichayontvijit, 2010. "Recommended play and performance bonuses in the minimum effort coordination game," Experimental Economics, Springer;Economic Science Association, vol. 13(3), pages 346-363, September.
    16. Croson, Rachel & Fatas, Enrique & Neugebauer, Tibor & Morales, Antonio J., 2015. "Excludability: A laboratory study on forced ranking in team production," Journal of Economic Behavior & Organization, Elsevier, vol. 114(C), pages 13-26.
    17. Goeree, Jacob K. & Holt, Charles A., 2005. "An experimental study of costly coordination," Games and Economic Behavior, Elsevier, vol. 51(2), pages 349-364, May.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    weak link game; minimum effort game; Nash equilibrium; beliefs;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary 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:gam:jgames:v:9:y:2018:i:3:p:42-:d:155312. 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: (XML Conversion Team). General contact details of provider: https://www.mdpi.com/ .

    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.